报告题目：Isoperimetric type inequalities for capillary surfaces

报告摘要：The study of capillary energies is a classical topic in Calculus of Variation. The course will start with a quick revue of basic definitions and properties of sets of finite perimeter. This will provide us with the tools needed to show the existence of minimizers for the capillary energy and to characterize the solution of the classical problem of the sessile drop sitting on a half space. Then we will present a new shorter proof of a well known isoperimetric type result of Choe-Ghomi and Ritoré, stating that half balls are the unique minimizers of the relative isoperimetric inequality outside a convex set. We will also discuss the same problem in the case of capillary surfaces with a general contact angle lying outside convex infinite cylinders. In particular we will see that the capillary energy of any surface supported on any such convex cylinder is strictly larger than that of a spherical cap with the same volume and the same contact angle on a flat support, unless the surface is itself a spherical cap resting on a facet of the cylinder. We will conclude the course by presenting some recent results on the behaviour of the isoperimetric profile in the exterior of a convex body for large volumes.

报告人简介：Nicola Fusco，意大利那不勒斯费德里科二世大学与南方高等学院（Scuola Superiore Meridionale）数学分析正教授、意大利林琴科学院（Accademia dei Lincei）院士、那不勒斯国家科学文学艺术院院士、2008年欧洲数学大会与2010年国际数学家大会ICM特邀报告人。2017--2020年担任欧洲数学会（EMS）执委，2017--2021年GNAMPA主任。2013-2016年任芬兰于韦斯屈莱大学"Finnish Distinguished Professor"。1995年获意大利数学会Caccioppoli 奖、2010年获林琴 Tartufari奖、2013年获Amerio奖。长期任 Adv. Calc. Var.、SIAM J. Math. Anal.、NoDEA 等期刊编委/主编，是尖锐定量等周不等式方面的主要奠基人之一，在数学领域四大顶刊之一Ann. of Math.等发表高水平论文100余篇，与Ambrosio、Pallara 合著该领域经典专著。

报告时间：

报告地点：同析4号楼308