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Remarks on a mean field equation on $mathbb{S}^{2}$

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 نشر من قبل Fengbo Hang
 تاريخ النشر 2019
  مجال البحث
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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 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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