The sphere covering inequality and Its Application to a Moser-Trudinger type inequality

Speaker:     Prof. Gui Changfeng (Univ. Texas at San Antonio and Hunan Univ.)

Time：  2017.8.10（Thursday）  16:00-17:00

Place： N613

Abstract：  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.