Remarks on a mean field equation on \mathbbS²

2019/05/26 by Changfeng Gui, Fengbo Hang, Gui, Changfeng +5
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.1905.10842

Abstract

In this note, we study symmetry of solutions of the elliptic equation -Δ_\mathbbS²u+3=e^2u \hboxon \mathbbS², that arises in the study of rigidity problem of Hawking mass in general relativity. We provide various conditions under which this equation has only constant solutions, and consequently imply the rigidity of Hawking mass for stable constant mean curvature (CMC) sphere.

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