Published Paper

Inserted: 8 mar 2023
Last Updated: 15 dec 2025

Journal: Journal für die reine und angewandte Mathematik
Year: 2025
Doi: https://doi.org/10.1515/crelle-2025-0065

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.