## Rigidity and compactness with constant mean curvature in warped product manifolds

created by maggi on 08 Mar 2023

[BibTeX]

preprint

Inserted: 8 mar 2023
Last Updated: 8 mar 2023

Year: 2023

ArXiv: 2303.03499 PDF

Abstract:

We prove the rigidity of rectifiable boundaries with constant distributional mean curvature in the Brendle class of warped product manifolds (which includes important models in General Relativity, like the deSitter--Schwarzschild and Reissner--Nordstrom manifolds). As a corollary we characterize limits of rectifiable boundaries whose mean curvatures converge, as distributions, to a constant. The latter result is new, and requires the full strength of distributional CMC-rigidity, even when one considers smooth boundaries whose mean curvature oscillations vanish in arbitrarily strong $C^k$-norms.