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 Events
Columbia University
Tue 4 Apr 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (PIMS)
Regularity of the Gauss curvature flow
ESB 2012 (PIMS)
Tue 4 Apr 2017, 3:30pm-4:30pm

Abstract

We will discuss about the regularity of the Gauss curvature flow: the optimal $C^{1,\frac{1}{n-1}}$ regularity of degenerate solutions with flat sides and the interior $C^{\infty}$ regularity of strictly convex solutions. 
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U.C. Santa Barbara
Tue 11 Apr 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Min-max minimal hypersurfaces with free boundary
ESB 2012
Tue 11 Apr 2017, 3:30pm-4:30pm

Abstract

I will present a joint work with Martin Li. Minimal surfaces with free boundary are natural critical points of the area functional in compact smooth manifolds with boundary. In this talk, I will describe a general existence theory for minimal surfaces with free boundary. In particular, I will show the existence of a smooth embedded minimal hypersurface with free boundary in any compact smooth Euclidean domain. The minimal surfaces with free boundary were constructed using the min-max method. I will explain the basic ideas behind the min-max theory as well as our new contributions.
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Université de Montpellier, France
Fri 12 May 2017, 1:00pm
Diff. Geom, Math. Phys., PDE Seminar
Time and Location TBA
Prescribing the curvature of hyperbolic convex bodies
Time and Location TBA
Fri 12 May 2017, 1:00pm-2:00pm

Abstract

 The Gauss curvature of a convex body can be seen as a measure on the unit sphere (with some properties). For such a measure $\mu$, Alexandrov problem consists in proving the existence of a convex body whose curvature measure is $\mu$. In the Euclidean space, this problem is equivalent to an optimal transport problem on the sphere.
 
In this talk I will consider Alexandrov problem for convex bodies of the hyperbolic space. After defining the curvature measure, I will explain how to relate this problem to a non linear Kantorovich problem on the sphere and how to solve it.
 
Joint work with J\’er\^ome Bertrand.
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