Convexity Seminar
Geometric Measure Equations, Optimizations, and PDEs in Convex Geometry
Time and Location:
Feb. 06, 2025 at 2PM; Warren Weaver Hall, Room TBASpeaker:
Gaoyong Zhang, Courant Institute, New York UniversityAbstract:
The Minkowski problem, which asks whether a convex body can be reconstructed from its surface area measure, was introduced and partially solved by Minkowski in the 1890's. A complete solution was given by Aleksandrov-Fenchel in the 1930s. Since the 1990s, there has been extensive work on answering this question for new geometric measures of a convex body. These Minkowski type problems are equivalent to Monge-Ampère PDEs in the smooth case, and are geometric measure equations in general. This talk will explain how the problems can be formulated as optimization problems and be solved by variational methods.