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

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Bibliographische Detailangaben
1. Verfasser:	Wang, Zhixin
Format:	Preprint
Veröffentlicht:	2025
Schlagworte:	Differential Geometry
Online-Zugang:	Acceder al recurso
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_version_	1866908329236758528
author	Wang, Zhixin
author_facet	Wang, Zhixin
contents	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}.
format	Preprint
id	arxiv_https___arxiv_org_abs_2504_15048
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Neumann Data and Second Variation Formula of Renormalized Area for Conformally Compact Static Spaces Wang, Zhixin Differential Geometry 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}.
title	Neumann Data and Second Variation Formula of Renormalized Area for Conformally Compact Static Spaces
topic	Differential Geometry
url	https://arxiv.org/abs/2504.15048

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