TY - JOUR
T1 - Remarks on a Mean Field Equation on $\mathbb{S}^2$
AU - Gui , Changfeng
AU - Hang , Fengbo
AU - Moradifam , Amir
AU - Wang , Xiaodong
JO - Journal of Mathematical Study
VL - 1
SP - 81
EP - 88
PY - 2021
DA - 2021/01
SN - 54
DO - http://doi.org/10.4208/jms.v54n1.21.04
UR - https://global-sci.org/intro/article_detail/jms/18599.html
KW - Semilinear elliptic equation, sphere covering inequality, rigidity of Hawking mass.
AB - <p style="text-align: justify;">In this note, we study symmetry of solutions of the elliptic equation</p><p style="text-align: justify;">\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.</p>