\(H\)-bubbles with prescribed large mean curvature
type: Item
instance of: scholarly article
title: \(H\)-bubbles with prescribed large mean curvature
zbMATH Open document ID: 1055.53004
author: Paolo Caldiroli
published in: Manuscripta Mathematica
publication date: 2004-03-11T00:00:00Z
review text: For a smooth real-valued function \(H\) on \(\mathbb{R}^3\) an \(H\)-bubble is a conformally immersed 2-sphere with mean curvature \(H\) at every point. It is shown that for any nondegenerate stationary point \(p\) of \(H\) with \(H(p)\neq 0\) there exists a family of embedded \(tH\)-bubbles for large \(t\), which become round and concentrate at \(p\) for \(t\to\infty\). The nondegeneracy can be replaced by some kind of topological stability in case of extremal points. The proofs use a perturbation method.
reviewed by: Erhard Heil
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 49J10
zbMATH DE Number: 2055255
zbMATH Keywords: \(H\)-bubbles
zbMATH Keywords: prescribed mean curvature
MaRDI profile type: Publication
full work available at URL: s00229-003-0427-8
OpenAlex ID: W2046544490
DOI: 10.1007/S00229-003-0427-8
description: scientific article; zbMATH DE number 2055255