Calculus of Variations and Geometric Measure Theory

F. Maggi - M. Santilli

Rigidity and compactness with constant mean curvature in warped product manifolds

created by maggi on 08 Mar 2023



Inserted: 8 mar 2023
Last Updated: 8 mar 2023

Year: 2023

ArXiv: 2303.03499 PDF


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.