Rigidity and bifurcation results for CMC hypersurfaces in warped product spaces
arXiv:1407.7500
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.
15 Pages, 1 Figure