Free boundary minimal hypersurfaces with least area
type: Item
instance of: scholarly article
title: Free boundary minimal hypersurfaces with least area
author: Qiang Guang
author: Zhichao Wang
author: Xin Zhou
published in: Communications in Analysis and Geometry
publication date: 2024-09-05T00:00:00Z
review text: Let \(M\) be a compact orientable Riemannian manifold with boundary \(\partial M\). Free boundary minimal hypersurfaces in \(M\) have zero mean curvature and their boundaries meet \(\partial M\) orthogonally. Suppose \(3\leq \dim M \leq 7\). Let \(\mathcal{O}\) (resp. \(\mathcal{U}\)) be the set of embedded compact orientable (resp. non-orientable) free boundary minimal hypersurfaces in \(M\). Then building on [\textit{L. Mazet} and \textit{H. Rosenberg}, J. Differ. Geom. 106, No. 2, 283--316 (2017; Zbl 1404.53078)], the authors show that there exists an embedded compact free boundary minimal hypersurface in \(M\) which attains the infimum of the sum of \(\{\mathrm{Area}\,(\Sigma ) \ | \ \Sigma \in \mathcal{O} \}\) and \(\{ 2\,\mathrm{Area}\,(\Sigma ) \ | \ \Sigma \in \mathcal{U} \}\).
reviewed by: Naoya Ando
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 7906843
zbMATH Keywords: free boundary minimal hypersurface
zbMATH Keywords: mini-max method
MaRDI profile type: Publication
DOI: 10.4310/CAG.2023.V31.N5.A4
description: scientific article; zbMATH DE number 7906843