Remarks on a Mean Field Equation on S2

Changfeng Gui; Fengbo Hang; Amir Moradifam; Xiaodong Wang

doi:10.4208/jms.v54n1.21.04

Remarks on a Mean Field Equation on S²

Changfeng Gui, Fengbo Hang, Amir Moradifam, Xiaodong Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this note, we study symmetry of solutions of the elliptic equation −∆_S²u+3=e^2u on S², that arises in the consideration 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.

Original language	English (US)
Pages (from-to)	81-88
Number of pages	8
Journal	Journal of Mathematical Study
Volume	54
Issue number	1
DOIs	https://doi.org/10.4208/jms.v54n1.21.04
State	Published - 2021

Keywords

rigidity of Hawking mass
Semilinear elliptic equation
sphere covering inequality

ASJC Scopus subject areas

General Mathematics

Access to Document

10.4208/jms.v54n1.21.04

Cite this

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AU - Moradifam, Amir

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KW - Semilinear elliptic equation

KW - sphere covering inequality

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