Work

Reilly inequality for varifolds

Year: 2026

Type: article

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.

Source: ESAIM Control Optimisation and Calculus of Variations

DOI: 10.1051/cocv/2026028

Authors: Jean-François Grosjean, Antoine Lemenant, Rémy Mougenot

Institutions: Institut Élie Cartan de Lorraine, Université de Lorraine

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4415255033

FWCI:

Cites:

Cited by:

Related to: