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.

叶德平（Deping Ye），加拿大Memorial University终身教授。2000年本科毕业于山东大学，2009年博士毕业于美国Case Western Reserve University。长期从事凸几何分析、几何不等式等领域的研究，在《Comm. Pure Appl. Math.》《Adv. Math.》等国际著名期刊发表论文40余篇。