Abstract: We introduce a functional involving weighted volume of convex bodies and their dual bodies and discuss the existence of critical points. When the ambient space is the sphere, finding critical criticals is equivalent to solving the Minkowski problem in the sphere (i.e., prescribing the Gauss curvature in the sphere). When the ambient space is the Euclidean space, a critical point corresponds to a solution to the prescribed centro-affine curvature problem. By using Gauss curvature flow and a variational method, we discuss the existence of origin-symmetric solutions. A crucial ingredient in our proof is a topological argument based on the study of a topological space of ellipsoids.
Speaker：
Qiang Guang
Dr. Qiang Guang is currently an MSI fellow at the Australian National University. He obtained his Ph.D. at Massachusetts Institute of Technology in 2016 under the supervision of William Minicozzi II. From 2016 to 2019, he was a Visiting Assistant Professor at University of California Santa Barbara. His research interests lie in Geometric Analysis and Geometric PDEs, particularly, minimal surfaces, mean curvature flow, and prescribing Gauss curvature problems in convex geometry.
Zoom:
https://us02web.zoom.us/j/88274650599?pwd=ZEE2bzl6bDR6bWtwTVZkSE9heU1TQT09
ID: 882 7465 0599
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