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Ailana M. Fraser

Professor

AF

Department of Mathematics
University of British Columbia
121 - 1984 Mathematics Road
Vancouver, BC V6T 1Z2

Email: afraser@math.ubc.ca
Phone: (604) 822-2785
Fax: (604) 822-6074

Office: Math Annex 1226

Research: Differential Geometry, Geometric Analysis

Selected Honours:

Fellow of the Canadian Mathematical Society, 2018-

Fellow of the American Mathematical Society, 2012-

CMS 2012 Krieger-Nelson Prize

NSERC Discovery Accelerator Supplement, 2010-2013

NSERC University Faculty Award, 2002-2007

Recent Events Co-organized:

2020 CMS 75th Anniversary Summer Meeting, Ottawa, June 5-8, 2020

PIMS Workshop on Geometric Anlaysis, UBC, May 18-19, 2019

Pacific Northwest Geometry Seminar, UBC, March 3-4, 2018

PIMS CRG Conference on Geometric Analysis, UBC, July 24-28, 2017

CMS Winter Meeting, Session on Differential Geometry, Montreal, Dec 4-7, 2015

Women in Geometry Workshop held at Banff International Research Station, November 1-6, 2015. Here is the Women in Geometry Workshop webpage.

Selected Publications:

Some results on higher eigenvalue optimization (with R. Schoen), arXiv:1910.03547.

Existence and classification of S^1-invariant free boundary annuli and Mobius bands in B^n (with P. Sargent), arXiv:1910.03238.

Shape optimization for the Steklov problem in higher dimensions (with R. Schoen), Advances in Mathematics 348 (2019), 146-162.

Existence of harmonic maps into CAT(1) spaces (with C. Breiner, L.-H. Huang, C. Mese, P. Sargent, Y. Zhang), to appear in Communications in Analysis and Geometry special issue in honor of Prof. Uhlenbeck's 75th birthday.

Regularity of Harmonic Maps from Polyhedra to CAT(1) Spaces (with C. Breiner, L.-H. Huang, C. Mese, P. Sargent, Y. Zhang), Calculus of Variations and Partial Differential Equations 57 (2018), no. 1, 1-35.

Mean curvature in manifolds with Ricci curvature bounded from below (with J. Choe), Commentarii Mathematici Helvetici 93 (2018), no.1, 55-69.

Sharp eigenvalue bounds and minimal surfaces in the ball (with R. Schoen), Inventiones Mathematicae 203(3) (2016), 823-890.

Uniqueness theorems for free boundary minimal disks in space forms (with R. Schoen), International Mathematics Research Notices (2015), no. 17, 8268-8274.

Minimal immersions of compact bordered Riemann surfaces with free boundary (with J. Chen, C. Pang), Transactions of the American Mathematical Society 367 (2015), 2487-2507.

Compactness of the space of embedded minimal surfaces with free boundary in three-manifolds with non-negative Ricci curvature and convex boundary (with M. Li), Journal of Differential Geometry 96 (2014), no.2, 183-200.

Minimal surfaces and eigenvalue problems (with R. Schoen), Contemporary Mathematics 599 (2013), 105-121.

Minimal surface techniques in Riemannian geometry, Surveys in Geometric Analysis and Relativity, Advanced Lectures in Mathematics 20, International Press (2011), 205-219.

The first Steklov eigenvalue, conformal geometry, and minimal surfaces (with R. Schoen), Advances in Mathematics 226 (2011), no. 5 4011-4030.

Holomorphic variations of minimal disks with boundary on a Lagrangian surface (with J. Chen), Canadian Journal of Mathematics 62 (2010), no. 6 1264-1275.

On stable minimal disks in manifolds with nonnegative isotropic curvature (with J. Chen), Journal fur die Reine und Angewandte Mathematik 643 (2010), 21-37.

Index estimates for minimal surfaces and k-convexity, Proceedings of the American Mathematical Society 135 (2007), no. 11 3733-3744.

The fundamental group of manifolds of positive isotropic curvature and surface groups (with J. Wolfson), Duke Mathematical Journal 133 (2006), no.2 325-334.

Fundamental groups of manifolds with positive isotropic curvature, Annals of Mathematics 158 (2003), no. 1 345-354.

Minimal disks and two-convex hypersurfaces, American Journal of Mathematics 124 (2002), no.3 483-493.

On the free boundary variational problem for minimal disks, Communications on Pure and Applied Mathematics 53 (2000), no. 8 931-971.