Stable hypersurfaces with constant mean curvature in \(R^ n\)
type: Item
instance of: scholarly article
title: Stable hypersurfaces with constant mean curvature in \(R^ n\)
zbMATH Open document ID: 0883.53008
author: Juan-Miguel Gracia
published in: Hiroshima Mathematical Journal
publication date: 1998-03-23T00:00:00Z
review text: The author proves that if \(M\) is a complete noncompact stable hypersurface in Euclidean space \(\mathbb{R}^n\) with constant mean curvature and nonnegative Ricci curvature, then \(M\) is a plane. This result partially answers do Carmo's conjecture that a complete noncompact stable hypersurface in \(\mathbb{R}^n\) with constant mean curvature is minimal.
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 986944
zbMATH Keywords: mean curvature
zbMATH Keywords: Ricci curvature
zbMATH Keywords: stability
zbMATH Keywords: minimal surface
reviewed by: Yanglian Pan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206127261
OpenAlex ID: W1567913793
DOI: 10.32917/HMJ/1206127261
description: scientific article; zbMATH DE number 986944