Perturbing away higher dimensional singularities from area minimizing hypersurfaces
type: Item
instance of: scholarly article
title: Perturbing away higher dimensional singularities from area minimizing hypersurfaces
zbMATH Open document ID: 0843.58025
author: Nathan Smale
author: Rafe Mazzeo
published in: Communications in Analysis and Geometry
publication date: 1996-01-01T00:00:00Z
review text: Let \(C\subset \mathbb{R}^{n+1}\) denote a strictly minimizing hypercone with an isolated singularity and \(C_1\) its truncation to the unit ball. \(\Sigma \subset S^n\) denotes its boundary link. Consider a compact \(k\)-dimensional Riemannian manifold. Then \(T_0= C_1 \times M\) is minimizing in \(\mathbb{R}^{n+1} \times M\), has boundary \(\Sigma \times M\) and singular set \(\{0\} \times M\). The authors now introduce the notion of one sided perturbations of \(\Sigma \times M\) as certain classes of submanifolds \(Z\) of dimension \(n+k-1\) in \(S^n \times M\) which are \(C^{1,\alpha}\) close to \(\Sigma \times M\) and show smoothness of the minimizer spanning \(Z\).
Mathematics Subject Classification ID: 58E12
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 820221
zbMATH Keywords: minimizing hypersurfaces
zbMATH Keywords: tangent cones
zbMATH Keywords: singularities
reviewed by: M. Fuchs
MaRDI profile type: Publication
DOI: 10.4310/CAG.1994.V2.N2.A7
description: scientific article; zbMATH DE number 820221