A barrier principle at infinity for varifolds with bounded mean curvature

Our work investigates varifolds \(\Sigma \subset M\) in a Riemannian manifold, with arbitrary codimension and bounded mean curvature, contained in an open domain \(\Omega\). Under mild assumptions on the curvatures of \(M\) and on \(\partial \Omega\), also allowing for certain singularities of \(\pa...

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Authors: Eddygledson Souza Gama, Jorge H S de Lira, Mari, Luciano, de Medeiros, Adriano A
Format: Article
Language:English
Subjects:
Curvature
Infinity
Riemann manifold
Online Access:Get full text
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Summary:Our work investigates varifolds \(\Sigma \subset M\) in a Riemannian manifold, with arbitrary codimension and bounded mean curvature, contained in an open domain \(\Omega\). Under mild assumptions on the curvatures of \(M\) and on \(\partial \Omega\), also allowing for certain singularities of \(\partial \Omega\), we prove a barrier principle at infinity, namely we show that the distance of \(\Sigma\) to \(\partial \Omega\) is attained on \(\partial \Sigma\). Our theorem is a consequence of sharp maximum principles at infinity on varifolds, of independent interest.
ISSN:2331-8422
DOI:10.48550/arxiv.2004.08946