General curvature estimates for stable \(H\)-surfaces immersed into a space form
type: Item
instance of: scholarly article
title: General curvature estimates for stable \(H\)-surfaces immersed into a space form
zbMATH Open document ID: 0960.53033
DOI: 10.1016/S0021-7824(99)00025-2
author: L. Hauswirth
author: Pierre Bérard
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1999-10-05T00:00:00Z
review text: Let \(M\) be a stable constant mean curvature \(H\) surface immersed in the simply connected 3-manifold \(\overline{M}(c)\) with constant curvature \(c.\) Using ideas as in \textit{R. Schoen} [Ann. Math. Stud. 103, 111-126 (1983; Zbl 0532.53042)], the authors derive estimates for the norm of the traceless second fundamental form and the Gaussian curvature at the center of a relatively compact geodesic ball with the stability operator bounded from below. These estimates imply that the two notions of weak and strong Morse indices coincide for complete noncompact constant mean curvature surfaces and that a complete stable constant mean curvature \(1\) surface in the usual hyperbolic space is a horosphere, which was proved by \textit{A. da Silveira} [Math. Ann. 277, 629-638 (1987; Zbl 0627.53045)].
reviewed by: Sung-Eun Koh
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 1344448
zbMATH Keywords: constant mean curvature
zbMATH Keywords: curvature estimate
zbMATH Keywords: stability
zbMATH Keywords: Morse index
MaRDI profile type: Publication
full work available at URL: s0021-7824(99)00025-2
OpenAlex ID: W4299555070
Wikidata QID: Q127933108
description: scientific article; zbMATH DE number 1344448