An existence result for minimal spheres in manifolds with boundary
type: Item
instance of: scholarly article
title: An existence result for minimal spheres in manifolds with boundary
zbMATH Open document ID: 0703.58014
author: Edi Rosset
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/244242
review text: In [Ann. Math. (2) 113, 1--24 (1981; Zbl 0462.58014)] \textit{J. Sacks} and \textit{K. Uhlenbeck} have proved the existence of a not homotopically trivial minimal sphere in Riemannian manifolds without boundary, having nontrivial second homotopy group. The author extends this result to a 3-manifold with boundary, obtained by deleting an open connected subset from the interior of a compact Riemannian oriented 3-manifold with smooth boundary and having trivial second homotopy group.
reviewed by: Enrique Outerelo
Mathematics Subject Classification ID: 58E12
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 4153513
zbMATH Keywords: minimal surface
zbMATH Keywords: pull back
zbMATH Keywords: Hodge *-operator
zbMATH Keywords: winding number
zbMATH Keywords: minimal sphere
zbMATH Keywords: 3-manifold with boundary
zbMATH Keywords: trivial second homotopy group
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4153513