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arXiv · 1706.06766

Uniqueness of the Mean Field Equation and Rigidity of Hawking Mass

Yuguang Shi·Jiacheng Sun·Gang Tian·Dongyi Wei
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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 $4<\lambda \leq 8$. 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.

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Yuguang Shi, Jiacheng Sun, Gang Tian, Dongyi Wei. 2017-06-21. Uniqueness of the Mean Field Equation and Rigidity of Hawking Mass. https://arxiv.org/abs/1706.06766

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