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arXiv · 2507.08354

Reilly inequality for Varifolds

Jean-François Grosjean·Antoine Lemenant·Rémy Mougenot
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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 $L^2$-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 $H(2)$ varifolds and for polygons and we analyse the equality case.

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Jean-François Grosjean, Antoine Lemenant, Rémy Mougenot. 2025-07-11. Reilly inequality for Varifolds. https://arxiv.org/abs/2507.08354

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