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arXiv · 2510.07296

Some rigidity results for static three-manifolds with boundary and positive scalar curvature

Vladimir Medvedev
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Abstract

This paper studies three-dimensional compact static manifolds with boundary and positive scalar curvature. We prove that, under a suitable bound on the Ricci curvature, the orientable quotient of the Nariai static manifold with boundary $Nar_{-1,1}(\mathbb S^2)$ is the only such manifold with connected boundary, provided that the zero-level set of the potential is connected and does not intersect the boundary. We also establish a rigidity theorem for the upper hemisphere with the standard static potential, in the spirit of Cruz and Nunes.

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Vladimir Medvedev. 2025-10-08. Some rigidity results for static three-manifolds with boundary and positive scalar curvature. https://arxiv.org/abs/2510.07296

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