欢迎光临!
您现在所在的位置:首页 >> 通知公告 & 学术信息
学术信息
SEMINARS
The Sphere Covering Inequality and its applications
时间  Datetime
2018-08-10 16:00 — 17:00 
地点  Venue
Middle Lecture Room
报告人  Speaker
Changfeng Gui
单位  Affiliation
University of Texas at San Antonio and Central South University
邀请人  Host
李从明
报告摘要  Abstract

In this talk, I will introduce a new geometric inequality:  the Sphere Covering Inequality. The inequality states that the total area of two {\it distinct}  surfaces with Gaussian curvature less than 1,  which  are also conformal to the Euclidean unit disk  with the same conformal factor on the boundary,  must be at least $4 \pi$.  In other words,  the areas of these surfaces must cover the whole unit sphere after a proper rearrangement. We apply the Sphere Covering Inequality to show the best constant of a Moser-Trudinger type inequality conjectured by A. Chang and P. Yang. Other applications of this inequality include the classification of certain Onsager vortices  on the sphere,  the radially symmetry of solutions to Gaussian curvature equation on the plane, classification of solutions for mean field equations on flat tori and  the standard sphere, etc. The resolution of several open problems in these areas will  be presented.  

 

The talk is based on joint work with Amir Moradifam from UC Riverside.