YoungHeon
Kim’s Research Home Teaching
Here
is my Brief
CV.
Research Interests: Partial Differential Equations and
Geometric Analysis:
Analysis and Geometry of Optimal
Transportation / MongeAmpere Equations (some
references)
Evolution equations and applications.
Variational calculus.
Riemannian Geometry
Spectral Geometry: Analytic Torsion (Determinants of Laplacians),
Isospectrality
Analysis of Riemann surfaces (Teichmueller Theory)
Inverse Problems
Mathematical economics
Collaborators
(in alphabetical order):
Xiaohui Chen
Alessio Figalli Hyunseok Kim
Seick
Kim Jun Kitagawa
Robert McCann
Emanuel Milman
Hanjin Lee Brendan
Pass Jeff Streets
Micah
Warren Jane Wang
Publications & Preprints:
 Prohibiting isolated singularities in optimal transport, with
Jun Kitagawa. Submitted. March. 2014.
 On weak solutions of linear elliptic equations with singular
drift terms, with Hyunseok Kim.
Submitted. March 2014.
 A general condition
for Monge solutions in the multimarginal optimal transport
problem, with Brendan
Pass. Submitted. July 24, 2013.To appear in SIAM J.
Math. Anal.
 Multimarginal
optimal transport on Riemannian manifolds, with Brendan Pass.
Submitted. March 2013.
 On
the degeneracy of optimal transportation, with Jun Kitagawa.
Submitted. Jan. 2013. To appear in Communications in Partial
Differential Equations.
 On
supporting hyperplanes to convex bodies, with Alessio Figalli
and Robert J. McCann.
To appear in Methods Appl. Anal.

Hoelder
continuity
and injectivity of optimal maps,with Alessio Figalli
and Robert J. McCann.
Arch. Rational Mech. Anal. 209 (2013)
747795. This paper supercedes the previous paper "Continuity
and injectivity for optimal maps with nonnegatively
crosscurved costs" below.
 Efficient minimax estimation of
highdimensional sparse precision matrices, with Xiaohui Chen and Z. Jane Wang. IEEE Transactions on Signal
Processing, Vol. 60, No. 6, June 2012: 2899 2912.
 Parabolic optimal
transport equations on manifolds, with Jeff Streets
and Micah
Warren. Int Math Res Notices (2012) Vol.
2012 43254350 first published online October 3, 2011
doi:10.1093/imrn/rnr188
 Regularity
of optimal transport maps on multiple products of spheres,
with Alessio
Figalli and Robert J. McCann.
J. Eur. Math. Soc. (JEMS) 15 (2013) 11311166.
 A generalization of
Caffarelli's contraction theorem via (reverse) heat flow,
with Emanuel
Milman. Math. Ann. 354 (3), 827862, 2012
 Partial regularity of Brenier solutions of the
MongeAmpère equation, with Alessio
Figalli. Discrete
Contin. Dyn. Syst. Series A, 28 (2010), no. 2, 559565.
 When
is multidimensional screening a convex program?
with Alessio
Figalli and Robert J. McCann.
J. Econom. Theory 146 (2011) 454478.
 Continuity
and injectivity for optimal maps with nonnegatively
crosscurved costs with Alessio Figalli
and Robert J. McCann.
Submitted. Nov. 2009 (superseded by a more recent paper Hoelder
continuity and injectivity of optimal maps, listed above).
 PseudoRiemannian
geometry
calibrates optimal transportation, with Robert J. McCann
and Micah
Warren. Math. Res. Lett. 17 (2010) 11831197
 Towards
the
smoothness of optimal maps on Riemannian submersions and
Riemannian products (of round spheres in particular), with
Robert J. McCann
. J. Reine Angew. Math.
(Crelle's journal), (2012), vol 664, 127
 Counterexamples
to continuity of optimal transportation on positively curved
Riemannian manifolds. International
Mathematics
Research Notices (2008) Vol. 2008 : article ID rnn120,
15 pages, doi:10.1093/imrn/rnn120.
 Curvature
and continuity of optimal transport, with Robert J. McCann.
An extended abstract. Oberwolfach
Report 35/2007:2629.
 Continuity,
curvature, and the general covariance of optimal
transportation, with Robert J. McCann.
J. Eur. Math. Soc. (JEMS) 12 (2010) 10091040.
 Surfaces
with boundary: their uniformizations, determinants of
Laplacians, and isospectrality. Duke Mathematical Journal, vol 144, no. 1 (2008) 73107.
 Holomorphic
Extensions
of Laplacians and Their Determinants. Advances in Mathematics 211(2007)
517545. (This is the paper version of my thesis for my PhD
degree for Northwestern University in 2005. My thesis advisor
was Ezra Getzler.)
 Determinants
of Laplacians, quasifuchsian spaces, and holomorphic
extensions of Laplacians. In the Tradition of
AhlforsBers, IV, Contemporary
Mathematics 432
(2007) 143150. (A summary of my thesis.)
 Harmonic maps into open manifolds with nonnegative curvature,
with JinWhan Yim. Commun.
Korean Math. Soc. 11
(1996) no.3, 789796.
Some unpublished
manuscripts:
Presentation
Slides
ETC
Conference/workshop
organizing:
 Analysis
and PDE July 712, 2013. "Conference in the honor
of the 60th birthday of Nassif Ghoussoub". University of
British Columbia, Vancouver, Canada. With Stephen Gustafson
(UBC), Dong Li (UBC), Abbas Moameni (Lethbridge), TaiPeng Tsai
(UBC), Juncheng Wei (UBC), Meijun Zhu (Oklahoma).
 Optimal
Transportation and Differential Geometry May 20 25,
2012. Banff International
Research Station (BIRS), Banff, AB, Canada. (with Alessio Figalli)
 PRIMAPARCPIMS
meeting in PDE. Dec. 78, 2010. University of British
Columbia, Vancouver, Canada. (with Nassif Ghoussoub, Stephen Gustafson and TaiPeng Tsai)
 Analysis
and Geometry of Nonlinear Partial Differential Equations.
Special session in Canadian Mathematical Society 2010 Winter Metting.
Dec 46. 2010, Vancouver, Canada. (with Nassif Ghoussoub and
Robert J. McCann.)
 Optimal
transportation and applications. April 1823, 2010. Banff International Research
Station (BIRS), Banff, AB, Canada. (with Alessio Figalli, Yuxin Ge,
Robert J. McCann
and Neil Trudinger.
)
 PIMS
Minisymposium in PDE, Nov. 1213, 2009. University of
British Columbia, Vancouver, Canada. (with Stephen Gustafson)
Invited
Talks and Lectures

 On degeneracy of optimal transportation. June 21, 2013.
Partial Differential Equations Seminar. Yonsei University,
Seoul, Korea.
 On a multimarginal optimal transport problem. June 20, 2013.
Mathematics Seminar. Korea Institute for Advanced Study. Seoul,
Korea.
 On a multimarginal optimal transport problem. June 17, 2013.
Partial Differential Equations Seminar. Korea Advanced Institute
of Science and Technology. Daejeon, Korea.
 On the degeneracy of optimal transportation. May 16, 2013.
Seminar “Analyse Numérique et E.D.P.” University of
ParisSud, Orsay. France.
 On a multimarginal optimal transport problem. May 7, 2013.
Seminaire "Dynamique et Géométrie".
Université de Nice Sophia Antipolis, Nice, France.
 On a multimarginal optimal transport problem. March 9, 2013.
Southern California Analysis & Partial Differential
Equations (SCAPDE) meeting, Mar 9 10, 2013, University of
California at Los Angeles, Los Angeles, CA.
 Hoelder continuity of optimal transport maps. August 6, 2012
Workshop “Recent trends in geometric and nonlinear analysis”,
August 510, 2012. Banff International Research Station, Banff,
AB.
 Hoelder continuity of optimal transport maps. July 23, 2012.
Workshop “Calculus of Variations”, July 2228, 2012.
Oberwolfach, Germany.
 Calibration, pseudoRiemannian geometry, and optimal
transportation. June 26, 2012. Mini workshop on geometry, June
25 –27, 2012. University of Montpellier, France.
 Hoelder continuity of optimal transport maps. June 21,
2012. Workshop “Optimal transport to Osray” June 1822.
University of ParisOrsay. France
 Dynamics to optimal transport. June 4, 2012. Conference
``Matching Problems: Economics Meets Mathematics” June 4—6,
University of Chicago, Chicago, IL, USA.
 Analysis and geometry in regularity of optimal maps.
April 27, 2012. Centre de Recherches Mathematiques, University
of Montreal, Montreal. (AndreAisenstadt Prize lecture)
 Parabolic optimal transport equations. Analysis seminar.
August 30, 2011. Yonsei University, Korea.
 Continuity of optimal transport maps and the curvature of Ma,
Trudinger and Wang. Three hour minicourse. August 29, 2011.
Seoul National University, Korea.
 Regularity of optimal transport maps. Workshop
“PRIMAPARCPIMS meeting in PDE”. August 25 –27, 2011. Seoul
National University, Korea
 Parabolic optimal transport equations. Analysis seminar.
August 24, 2011. KAIST, Korea.
 Regularity of optimal transport maps. Applied
Analysis and Applied PDEs. July 12  July 15, 2011.
Victoria, Canada.
 MaTrudingerWang curvature and regularity of optimal
transport. Invited Lecturer (4 series lectures): 50th SMS
2011.
Metric Measure Spaces: Geometric and Analytic Aspects.
June 27  July 8, 2011. Centre de Recherches Mathematiques,
Montreal, Quebec.
 Regularity of optimal transport maps on multiple products of
spheres.. The second renunion conference for IPAM’s
Optimal Transport Program. Dec. 1217, 2010. Lake Arrowhead,
CA.
 Regularity of optimal transport maps on multiple products of
spheres.. Workshop on Geometric Probability and Optimal
Transportation. Nov. 15, 2010 (tentative dates) Fields
Institute, Toronto. Canada.
 Regularity of optimal transport maps on multiple products of
spheres.. Optimal
Transportation and Applications. Oct. 12 16, 2010. SNS,
Pisa, Italy.
 Regularity of optimal transport maps on multiple products of
spheres. Sept. 3, 2010. SAGE
workshop: Optimal Transport and Riemannian Geometry
(BakryEmery curvature, MaTrudingerWang curvature, and
applications to Ricci flow). Sept. 13, 2010. U. Texas,
Austin, TX.
 Regularity of optimal transport maps on multiple products of
spheres. Aug. 16, 2010. Colloquium. University of Iowa. Iowa
City, IA.
 Regularity of optimal transport maps on multiple products of
spheres. July 22, 2010. Calculus
of Variations, July 1824, 2010. Oberwolfach, Germany.
 Regularity of optimal transport maps on multiple products of
spheres. July 14, 2010. FAWG seminar. U. Toronto, Toronto,
Canada.
 Nonnegatively crosscurved transportation costs, March, 22,
2010. International
Conference on Nonlinear PDE and Related Analysis/Applications
(in conunction with the 64th Midwest PDE seminar), March 2024,
2010. Northwestern University, Evanston, IL, USA.
 Nonnegatively crosscurved transportation costs. Dec
22, 2009. PDE Seminar. Sungkyunkwan University, Suwon, Korea.
 cMongeAmpere equations. Dec 21, 2009. PDE Seminar. Seoul
National University, Seoul, Korea.
 Nonnegatively crosscurved transportation costs, Dec 19,
2009. Joint meeting of
the Korean Mathematical Society and the American Mathematical
Society: special session  Nonlinear Partial
Differential Equations and Viscosity Solutions. (Dec. 1620,
2009)
 Nonnegatively crosscurved transportation costs, Dec 8, 2009.
The first reunion conference for IPAM’s
Optimal Transport Program. Dec. 611, 2009. Lake Arrowhead, CA.
 Nonnegatively crosscurved transportation costs, Nov 6, 2009.
University of
Washington, Seattle, WA.
 Nonnegatively crosscurved transportation costs, Oct 2,
2009. Praire
Analysis Seminar Oct 23, 2009 (a contribution talk).
Kansas State University, KS.
 Geometry and regularity of optimal transportation. June 1,
2009. Geometry/Physics seminar.Northwestern Univ.
Evanston. IL.
 Determinants of Laplacians as functions on spaces of
Riemannian metrics. March 9, 2009. Univ. of Maryland. College
Park, MD.
 Determinants of Laplacians as functions on spaces of
Riemannian metrics. Aug. 25, 2008. Seminar. Kyung Hee Univ.
Seoul, Korea.
 On continuity of optimal transportation. Aug. 22, 2008.
Seminar. Pohang Univ.
Sci. & Tech. Pohang,
Korea.
 Determinants of Laplacians as functions on spaces of
Riemannian metrics. Aug. 22, 2008. Seminar. Pohang Univ. Sci. &
Tech. Pohang, Korea.
 On continuity of optimal transportation. Aug. 8, 2008.
Seminar. Korea Adv.
Inst. Sci. & Tech. Daejun, Korea
 Analysis of surfaces. Aug. 6, 2008. Geometry seminar. Seoul National Univ.
Seoul, Korea.
 Continuity of optimal transportation. Aug. 5, 2008. PDE
seminar. Seoul
National Univ. Seoul, Korea.Curvature and continuity of
optimal transportation. July 2009.
 Curvature and continuity of optimal transportation. Workshop
on Transport, Optimization, Equilibrium in Economics. July
14  July 20, 2008. PIMS,
University of British Columbia, Vancouver, BC.
 Continuity of optimal transport maps under a degenerate MTW
condition. July 10, 2008. Calculus
of varations. Oberwolfach
workshop, Germany.
 Some geometric aspects of regularity of optimal
transportation. June 9, 2008. Optimal
Transport Culminating workshop at Lake Arrowhead.
IPAM. CA.
 Some geometric aspects of regulairty of optimal
transportation. May 2, 2008. Analysis and PDE seminar. UCLA, Los Angeles, CA.
 Curvature and continuity of optimal transport. Mar. 16, 2008.
AMS
2008
Spring Eastern Meeting, Mar. 1516, 2008 Special Session
on Nonlinear Elliptic Equations and Geometric
Inequalities. New York, NY.
 Curvature and continuity of optimal transport. Feb. 20, 2008.
Colloquium. University of Oregon,
Eugene, OR.
 Curvature and continuity of optimal transport. Feb. 18, 2008.
Colloquium. Simon Fraser University,
Vancouver, BC.
 Curvature and continuity of optimal transport. Jan 25 2008.
Colloquium. University of Arizona,
Tucson, AZ.
 Determinants of Laplacians as functions on spaces of metrics.
Jan. 17, 2008. Diff. Geom.Math. Phys.PDE Seminar. University
of British Columbia, Vancouver, BC.
 Curvature and continuity of optimal transport, Jan 16.
2008, Colloquium. University of British Columbia,
Vancouver, BC.
 Curvature and continuity of optimal transport. Jan. 15, 2008.
Colloquium. Lehman College
CUNY, New York, NY.
 Determinants of Laplacians as functions on spacecs of metrics.
Jan 12. 2008. Southern
California
Analysis/PDE Conference at UCSD. San Diego,
CA. (SatSun) January 1213, 2008.
 Curvature and continuity of optimal transport, Jan. 11, 2008.
Partial Differential Equations Seminar. UCSD, San Diego, CA.
 Curvature and continuity of optimal transport. Jan. 8, 2008. University of Edinburgh.
Edinburgh, UK.
 Curvature and continuity of optimal transport. Jan. 7, 2008. Hausdorff
Center for Mathematics. Bonn, Germany.
 Curvature and continuity of optimal transport. Dec. 2007. Canadian
Mathematical Society Winter 2007 Meeting, Dec. 8 10, 2007Special
session: Calculus of Variations in Physics, Geometry and
Economics. London, Ontario, Canada.
 Curvature and continuity of optimal transport. Nov. 2007. Prairie Analysis
Seminar 2007 Nov 23, 2007. (A contribution talk) Kansas State University,
Manhattan, Kansas.
 Curvature and the continuity of optimal transportation maps,
July 24, 2007, MSRI(Berkeley)Summer
Microprogram on Nonlinear Partial Differential Equations (July
23, 2007 to August 10, 2007 ).
 Curvature and the continuity of optimal transportation maps,
July 19, 2007, Conference Optimal
Transportation, and Applications to Geophysics and Geometry (Jul
16, 2007  Jul 20, 2007) , ICMS, University of Edinburgh.
 Determinants of Laplacians and isospectrality, July 10, 11,
& 12, 2007, KIAS
(Seoul) Summer
school
on
Dirac
and
Laplace
Operators
(Jul 09, 2007 ~ Jul 13, 2007).
 Determinants of Laplacians and their holomorphic extensions,
July 3, 2007, KIAS
(Seoul) Seminar.
 Curvature and the continuity of optimal transportation maps,
June 20, 2007, Banff workshop Geometric
Inequalities (Sun. June 17, 2007  Fri. June 22, 2007).
 Curvature and the continuity of optimal transportation maps,
April 13, 2007, Fields Institute, Young
Mathematicians' Conference in PDE and Dynamical Systems IV
(April 1314, 2007).
 Determinants
of Laplacians as functions on spaces of metrics,
Nov. 17, 2006, Princeton
University, Geometric
Analysis Seminar.
 Determinants of Laplacians and isospectrality of compact
surfaces with boundary, Oct. 30, 2006, University of
Waterloo,
Geometry/Topology Seminar.
 Determinants of Laplacians and their holomorphic
extensions,Apr. 18, 2006, Ohio State University,
Analysis/Geometry Seminar.
 Determinants of Laplacians and Quasifuchsian Spaces, Feb. 3,
2006, Northwestern
University, Geometry/Physics Seminar.
 Determinants of Laplacians and their holomorphic extensions ,
Feb. 2, 2006, University
of Chicago, Geometry/Topology Seminar.
 Determinants
of Laplacians and their holomorphic extensions, May
19, 2005, Workshop on The WeilPetersson Geometry of
Teichmuller Space, 2005
Ahlfors Bers Colloquium, University of Michigan, Ann
Arbor, Michigan.
 Holomorphic extensions of determinants of Laplacians, April 9,
2005 2005
Bloomington Geometry Workshop, Indiana University,
Bloomington, Indiana.
Local
Seminar Talks
 Nonnegatively crosscurved transportation costs. Nov. 24,
2009. DGMPPDE seminar. UBC, Vancouver, BC.
 Continuity of optimal transport maps under a degenerate MTW
condition. Dec. 2, 2008. Member seminar. Inst. for Advanced
Study. Princeton, NJ
 Curvature and the continuity of optimal transport maps, March
8, March 22, 2007 Fields
Analysis Working Group Seminar
 Determinants of Laplacians as functions on spaces of
metrics, Nov. 20, 2006, University of Toronto, Geometry
and Topology Seminar.
 Regularity results for optimal transport problems with general
costs , Oct. 26, Nov. 2, 2006. Fields
Analysis Working Group Seminar.
 Determinants of Laplacians and isospectrality of compact
surfaces with boundary. Oct. 13, 2006, University of
Toronto, PDE/Applied Math/Analysis Seminar.
 Determinants of Laplacians and their holomorphic extensions,
Nov. 17, 2005, Fields Insititute, Mini course.
Conferences
and Programs (which I have participated, will attend, or
am interested in since 2007)
 Southern
California Analysis & Partial Differential Equations
(SCAPDE) meeting, Mar 9 10, 2013, University of
California at Los Angeles, Los Angeles, CA.
 Workshop “Recent
trends in geometric and nonlinear analysis”, August 510,
2012. Banff International Research Station, Banff,
AB.
 Workshop “Calculus
of Variations”, July 2228, 2012. Oberwolfach, Germany.
 Mini workshop on geometry, June 25 –27, 2012. University of
Montpellier, France.
 Workshop “Optimal
transport to Osray” June 1822. University of
ParisOrsay. France
 Conference ``Matching
Problems: Economics Meets Mathematics” June 4—6,
University of Chicago, Chicago, IL, USA.
 Workshop “PRIMAPARCPIMS
meeting in PDE”. August 25 –27, 2011. Seoul National
University, Korea.
 Applied
Analysis and Applied PDEs. July 12  July 15, 2011.
Victoria, Canada.
 SMS
2011.
Metric
Measure
Spaces:
Geometric and Analytic Aspects. June 27  July 8, 2011.
Montreal, Canada.
 The second renunion conference for IPAM’s
Optimal Transport Program. Dec. 1217, 2010. Lake Arrowhead,
CA.
 PRIMAPARCPIMS
meeting in PDE. Dec. 7 8, 2010. UBC, Vancouver, Canada.
 CMS winter
meeting. Dec 4 6. 2010. UBC, Vancouver, Canada.
 Workshop
on Geometric Probability and Optimal Transportation. Nov.
15, 2010 (tentative dates) Fields Institute, Toronto.
Canada.
 Optimal
Transportation and Applications. Oct. 12 16, 2010. SNS,
Pisa, Italy.
 SAGE
workshop:
Optimal Transport and Riemannian Geometry (BakryEmery
curvature, MaTrudingerWang curvature, and applications to
Ricci flow). Sept. 13, 2010. U. Texas, Austin, TX.
 PRIMA
conference on Geometric Analysis. July 20 30,
2010. PIMS, UBC, Vancouver, Canada.
 Calculus of Variations, July
1824, 2010. Oberwolfach,
Germany.
 CNA
summer school. June 712, 2010. CarnegieMelon
University. Pittsburg, PA (Not attended)
 Optimal
transportation and applications. April 1823, 2010. Banff International Research
Station (BIRS), Banff, AB, Canada.
 International
Conference on Nonlinear PDE and Related Analysis/Applications
(in conunction with the 64th Midwest PDE seminar), March 2024,
2010. Northwestern University, Evanston, IL, USA.
 KMS AMS Joint meeting,
Dec. 1620, 2009. Seoul, Korea
 The first renunion conference for IPAM’s
Optimal Transport Program. Dec. 611, 2009. Lake Arrowhead, CA.
 Pacific
Northwest Geometry Seminar (Nov
78, Portland State U., Oregon)
 Fall
school on weak KAM.
Oct. 1923, 2009. CIRM.
Luminy, France.
 Prairie Analysis
Seminar. Oct.
23., 2009. Kansas State Univ. Manhattan, Kansas.
 PIMS
thematic program on PDE. June, July, Aug, 2009. UBC,
Vancouver, BC.
 Geometric Partial
Differential Equations. Sep 2008  April 2009. IAS,
Princeton, NJ.
 Workshop
on Transport, Optimization, Equilibrium in Economics. July
14  July 20, 2008. University of British Columbia, Vancouver,
BC.
 Calculus
of Variations,
July 6th  12th, 2008. Oberwolfach, Germany.
 2008 CNA Summer
School May 29 – June 7, 2008, Center for Nonlinear
Analysis, Carnegie Mellon University, Pittsburgh, PA (Not
attended)
 Optimal
Transport, March 10  June 13 2008, IPAM(UCLA).
 AMS
2008
Spring Eastern Meeting, Mar. 1516, 2008 (SatSun)
Special Session on Nonlinear Elliptic Equations and
Geometric Inequalities. New York, NY.
 Southern
California Analysis/PDE Conference at UCSD. San Diego,
CA. (SatSun) January 1213, 2008.
 Canadian
Mathematical Society Winter 2007 Meeting, Dec. 8 10, 2007.
Hilton Hotel London (Ontario, Canada) special session:
Calculus of Variations in Physics, Geometry and Economics.
 Prairie Analysis
Seminar 2007 (FriSat. Nov 23, 2007). Kansas State University,
Manhattan, Kansas.
 MSRI(Berkeley)
Summer
Microprogram on Nonlinear Partial Differential Equations
(July 23, 2007 to August 10, 2007 ). Berkeley, CA.
 ICMS (Edinburgh): Optimal
Transportation, and Applications to Geophysics and Geometry (Jul
16, 2007  Jul 20, 2007). Edinburgh, UK.
 KIAS
(Seoul) Summer
school on Dirac and Laplace Operators (Jul 09, 2007
~ Jul 13, 2007). Korea.
 Banff Geometric
Inequalities (Sun. June 17, 2007  Fri. June 22,
2007). Banff, Alberta, Canada.
 MPIM (Bonn, Germany)
(May 4, 2007  May 31, 2007).
 IPAM(UCLA): Random
Curves, Surfaces, and Transport. (April 16  20, 2007).
 Fields Institute, Toronto:Young
Mathematicians' Conference in PDE and Dynamical Systems IV
(April 1314, 2007).
Updated: March 2014