The sphere covering inequality and Its Application to a Moser-Trudinger type inequality
The sphere covering inequality and Its Application to a Moser-Trudinger type inequality
报 告 人: Prof. Gui Changfeng (Univ. Texas at San Antonio and Hunan Univ.)
时 间: 2017年8月10日(周四) 16:00-17:00
地 点: 数学院南楼613
摘 要: In this talk, The speaker will introduce a new geometric inequality: The sphere covering Inequality. The inequality states that the total area of two distinct surfaces with Gaussian curvature less than 1, which are also conformal to the Euclidean unit diskwith 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 in classification of certain Onsager vortices on the sphere, the radially symmetry of solutions to Gaussian curvature equation on the plane, classification on the flat tori and standard sphere,etc. The talk is based on joint work with Amir Moradifam from UC Riverside.