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arXiv · 2504.15048

Neumann Data and Second Variation Formula of Renormalized Area for Conformally Compact Static Spaces

Zhixin Wang
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Abstract

In this paper, we derive the first and second variation formulas for the renormalized area for static Einstein spaces along a specific direction, demonstrating that the negativity of the Neumann data implies instability. Consequently, we obtain a rigidity result for the case when the conformal boundary is a warped product torus, which strengthens the result presented in \cite{GSW}.

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Zhixin Wang. 2025-04-21. Neumann Data and Second Variation Formula of Renormalized Area for Conformally Compact Static Spaces. https://arxiv.org/abs/2504.15048

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