Rigidity and bifurcation results for CMC hypersurfaces in warped product spaces

TL;DR

This paper investigates the rigidity and bifurcation phenomena of constant mean curvature hypersurfaces in warped product spaces, revealing conditions for local rigidity and bifurcation points in specific spacetime models.

Contribution

It introduces new rigidity and bifurcation results for CMC hypersurfaces in warped product spaces, especially in Anti-de Sitter and de Sitter Schwarzschild spacetimes.

Findings

Existence of locally rigid one-parameter families in Anti-de Sitter Schwarzschild spacetime

Presence of bifurcation points in de Sitter Schwarzschild spacetime

Rigidity results under normal variations of CMC hypersurfaces

Abstract

In this paper, we deduce some rigidity results in warped product spaces under normal variations of CMC hypersurfaces. In particular, we prove the existence of one-parameter families locally rigid on the spatial fiber of Anti-de Sitter Schwarzschild spacetime and one-parameter families with bifurcation points on the spatial fiber of de Sitter Schwarzschild spacetime.