Volume and energy stability for isometric minimal immersions
type: Item
instance of: scholarly article
title: Volume and energy stability for isometric minimal immersions
zbMATH Open document ID: 0661.53040
author: Michael Hvidsten
published in: Illinois Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: It is well known that a minimal isometric immersion from a Riemannian manifold M into a Riemannian manifold N is also a harmonic immersion. The second order behavior of the volume and energy functionals is studied in this paper, and it is shown that in the case of codimension-one immersions into flat Riemannian manifolds, the immersions are always energy stable, but will be volume stable if and only if they are totally geodesic. Several examples of energy stable, but volume unstable minimal surfaces in the three-torus are then described. Similar results are given for minimal isometric immersions into manifolds of codimension greater than one, provided the target manifold is parallelizable.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 4080326
zbMATH Keywords: stability
zbMATH Keywords: volume
zbMATH Keywords: harmonic immersion
zbMATH Keywords: energy
zbMATH Keywords: totally geodesic
zbMATH Keywords: minimal surfaces
zbMATH Keywords: minimal isometric immersions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4080326