Uniqueness of the Mean Field Equation and Rigidity of Hawking Mass

Yuguang Shi, Jiacheng Sun, Gang Tian +1

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 s…