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
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Some geometric inequalities related to Liouville equation
Gui, Changfeng
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https://doi.org/10.1007/s00209-023-03369-5 [Citations: 0]