Uniqueness of the Mean Field Equation and Rigidity of Hawking Mass

Abstract

In this paper, we prove that the even solution of the mean field equation $\Delta u=\lambda (1-e^u)$ on $S^2$ must be axially symmetric when $4<\lambda \le 8$. In particular, zero is the only even solution for $\lambda =6$. This implies the rigidity of Hawking mass for stable constant mean curvature(CMC) sphere with even symmetry.

15 pages

Cited by in corpus (1)

• The sphere covering inequality and its dual