Morse theory for the area functional
type: Item
instance of: scholarly article
title: Morse theory for the area functional
zbMATH Open document ID: 1482.53080
author: André Neves
author: Fernando C. Marques
published in: São Paulo Journal of Mathematical Sciences
publication date: 2021-07-28T00:00:00Z
review text: This article is a survey on the path leading to a Morse-theoretic result for the area functional in codimension one, that is, any closed manifold of low dimension endowed with a smooth metric can be approximated with smooth, closed, embedded minimal hypersurfaces satisfying some properties. After a short historic introduction, it introduces the different tools needed to prove the central result of the survey. Namely, they need upper bounds on the index, lower bounds when multiplicities are equal to one and the multiplicity one conjecture (by now, a theorem). A sketch of the proofs follows.
reviewed by: Giorgio Saracco
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 58E12
Mathematics Subject Classification ID: 49Q20
Mathematics Subject Classification ID: 53-02
zbMATH DE Number: 7375685
zbMATH Keywords: geometric measure theory
zbMATH Keywords: area functional
zbMATH Keywords: Morse theory
zbMATH Keywords: minimal surfaces
zbMATH Keywords: volume spectrum
Wikidata QID: Q107168959
MaRDI profile type: Publication
full work available at URL: s40863-019-00159-y
OpenAlex ID: W2995844195
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DOI: 10.1007/S40863-019-00159-Y
description: scientific article; zbMATH DE number 7375685