【摘 要】
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In this talk, I will present a new inequality: the Sphere Covering Inequality. The inequality states that the total area of two distinct surfaces with Gauss
【机 构】
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UniversityofConnecticut,USA
【出 处】
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2016年非线性偏微分方程和变分方法及其应用研讨会(Workshop on Nonlinear PDEs and Cal
论文部分内容阅读
In this talk, I will present a new inequality: the Sphere Covering Inequality. The inequality states that the total area of two distinct surfaces with Gaussian curvature 1, which are also conformal to the Euclidean unit disk with the same conformal factor on the boundary, must be at least 4 . 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 eld equations on fl at tori and the standard sphere, etc. The resolution of several interesting problems in these areas will be presented. The work is jointly done with Amir Moradifam from UC Riverside.
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