Embedded minimal disks with a free boundary on a polyhedron in \({\mathbb R}^ 3\)
type: Item
instance of: scholarly article
title: Embedded minimal disks with a free boundary on a polyhedron in \({\mathbb R}^ 3\)
zbMATH Open document ID: 0633.53011
DOI: 10.1007/BF01159781
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173969
review text: We show that a convex polyhedron in Euclidean 3-space bounds an embedded minimal surface meeting this polyhedron orthogonally along its boundary. The minimal surface is nontrivial in the sense that it does not coincide with a face and does not contain an edge of the polyhedron in its boundary. The proof is based on previous results of the author for smooth free boundaries, a blow-up argument, and barrier constructions utilizing catenoids.
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 4030384
zbMATH Keywords: minimal surface
zbMATH Keywords: smooth free boundaries
zbMATH Keywords: catenoids
zbMATH Keywords: boundary on a polyhedron
author: Jürgen Jost
MaRDI profile type: Publication
cites work: Maximum principles for minimal surfaces and for surfaces of continuous mean curvature
cites work: Q3822750
cites work: Continuity of minimal surfaces with piecewise smooth free boundaries
cites work: Embedded minimal surfaces in manifolds diffeomorphic to the three-dimensional ball or sphere
cites work: Q4081953
OpenAlex ID: W2142760680
description: scientific article; zbMATH DE number 4030384