Remarks on a Mean Field Equation on $\mathbb{S}^2$

Remarks on a Mean Field Equation on $\mathbb{S}^2$

Year:    2021

Author:    Changfeng Gui, Fengbo Hang, Amir Moradifam, Xiaodong Wang

Journal of Mathematical Study, Vol. 54 (2021), Iss. 1 : pp. 81–88

Abstract

In this note, we study symmetry of solutions of the elliptic equation

\begin{equation*} -\Delta _{\mathbb{S}^{2}}u+3=e^{2u}\ \ \hbox{on}\ \ \mathbb{S}^{2},\end{equation*} 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v54n1.21.04

Journal of Mathematical Study, Vol. 54 (2021), Iss. 1 : pp. 81–88

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

Keywords:    Semilinear elliptic equation sphere covering inequality rigidity of Hawking mass.

Author Details

Changfeng Gui

Fengbo Hang

Amir Moradifam

Xiaodong Wang