Variation formulas for mean curvature functionals

Abstract

We establish first and second variation formulas for general mean curvature functionals under arbitrary variations in arbitrary Riemannian manifolds. We obtain corresponding formulas in the sub-Riemannian Heisenberg group through a Riemannian approximation scheme.

The material in this article previously appeared in Appendices A and B of arXiv:2605.29912v1, of which the present author is a coauthor. These appendices will be removed from a subsequent version of arXiv:2605.29912, which will instead refer to the present article