Convexity Seminar

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(NEW TIME) Optimal transport and the Gauss curvature equation

Speaker: Nestor Guillen, Texas State University

Location: Warren Weaver Hall 1314

Date: Thursday, February 20, 2025, 1 p.m.

Synopsis:

In joint work with Jun Kitagawa we consider the problem of prescribing both the Gauss curvature and the image of the Gauss map for a surface given as the graph of a function over a domain in Euclidean space. Our main observation is that this problem can be reformulated as an optimal transport problem between a domain in Euclidean space and a hemisphere of the unit sphere. This reformulation allows us to apply optimal transport theory and interpret and improve on existence and regularity results for the prescribed Gauss curvature equation. In particular, we obtain a quantitative improvement on a classical result by Urbas on gradient blow up at the boundary for solutions of the Gauss curvature equation.