Reilly inequality for Varifolds
Differential Geometry
2025-07-14 v1
Abstract
The famous Reilly inequality gives an upper bound for the first eigenvalue of the Laplacian defined on compact submanifolds of the Euclidean space in terms of the -norm of the mean curvature vector. In this paper, we generalize this inequality in a Varifold context. In particular we generalize it for the class of varifolds and for polygons and we analyse the equality case.
Cite
@article{arxiv.2507.08354,
title = {Reilly inequality for Varifolds},
author = {Jean-François Grosjean and Antoine Lemenant and Rémy Mougenot},
journal= {arXiv preprint arXiv:2507.08354},
year = {2025}
}