New \(r\)-minimal hypersurfaces via perturbative methods
type: Item
instance of: scholarly article
title: New \(r\)-minimal hypersurfaces via perturbative methods
zbMATH Open document ID: 1232.53053
author: L. L. de Lima
author: Juscelino Silva
author: Jorge H. S. de Lira
published in: The Journal of Geometric Analysis
publication date: 2011-11-14T00:00:00Z
review text: A hypersurface is called \(r\)-minimal if and only if the \((r+1)\)-th elementary symmetric function of its principal curvatures vanishes identically. Using the deformation theory in weighted Hölder spaces developed by Mazzeo, Pacard, Pollack and Uhlenbeck, the authors produce new infinite-dimensional families of \(r\)-minimal hypersurfaces of the \((n+1)\)-dimensional Euclidean space. These examples are obtained by perturbing noncompact portions of catenoids. The authors also consider the moduli space of elliptic \(r\)-minimal hypersurfaces with \(k \geq 2\) ends of planar type endowed with an ALE metric \(g\). They show that this is an analytic manifold of formal dimension \(k(n+1)\) which is smooth for a generic \(g\) in a neighborhood of the standard Euclidean metric.
reviewed by: Luc Vrancken
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 5971470
zbMATH Keywords: catenoids
zbMATH Keywords: \(r\)-minimal hypersurfaces
zbMATH Keywords: weighted Hölder spaces
zbMATH Keywords: ALE spaces
MaRDI profile type: Publication
full work available at URL: s12220-011-9244-6
OpenAlex ID: W1975914315
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DOI: 10.1007/S12220-011-9244-6
description: scientific article; zbMATH DE number 5971470