Minimal hypersurfaces of a positive scalar curvature manifold
type: Item
instance of: scholarly article
title: Minimal hypersurfaces of a positive scalar curvature manifold
zbMATH Open document ID: 0549.53059
DOI: 10.1007/BF01159165
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173611
review text: This is a systematic study of the placement question for minimal hypersurfaces in a manifold of positive scalar curvature. Among the results we prove that if \(\Sigma_ 1\coprod...\coprod\Sigma_ n\subset S^ 3\) are mutually disjoint minimal surfaces embedded in a 3-sphere of positive scalar curvature, then there exists a decomposition \(S^ 3=S^ 3\#...\#S^ 3\) with each \(\Sigma_ j\) in a distinct summand. The technique used gives a new and more elementary proof of the fact that a compact minimal surface \(\Sigma\) embedded in a 3-sphere of positive scalar curvature must be topologically standard. We also present a series of examples of immersed hypersurfaces in the n-sphere \(S^ n\) which can never be minimal for any metric of positive scalar curvature on \(S^ n\).
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 3876146
zbMATH Keywords: minimal hypersurfaces
zbMATH Keywords: positive scalar curvature
zbMATH Keywords: mutually disjoint minimal surfaces
zbMATH Keywords: 3-sphere
author: Sebastião Carneiro de Almeida
MaRDI profile type: Publication
Wikidata QID: Q124848589
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OpenAlex ID: W2077448324
description: scientific article; zbMATH DE number 3876146