几何分析讨论班

报告题目：The Gaussian Minkowski Problem for Epigraphs of Convex Functions

报 告 人：Deping Ye（Memorial University of Newfoundland）

时  间：2026年10月26日（星期一），下午16:00-17:00

地  点：海纳苑2幢205

摘  要：The Gaussian Minkowski problem lies at the intersection of convex geometry and Gaussian analysis, with deep connections to variational methods and partial differential equations. While the classical theory focuses on convex bodies, many important objects in analysis are naturally unbounded, such as the epigraph of convex functions.

In this talk, I will discuss a Gaussian Minkowski problem for epigraphs of convex functions. Using infimal convolution, we derive a variational formula for the Gaussian volume of epigraphs and define associated Gaussian moment measures for convex functions. We then formulate the corresponding Minkowski problem and establish existence results under natural assumptions on the prescribed measure. It provides a natural framework that connects convex geometry, functional inequalities, and Monge– Ampère equations, leading to new geometric questions in the Gaussian setting.