Maximum principle at infinity for complete minimal surfaces in flat 3-manifols
type: Item
instance of: scholarly article
title: Maximum principle at infinity for complete minimal surfaces in flat 3-manifols
zbMATH Open document ID: 0873.53039
DOI: 10.1007/BF01120326
author: Marc Soret
published in: Annals of Global Analysis and Geometry
publication date: 1995-08-02T00:00:00Z
review text: The author studies the maximum principle at infinity for minimal surfaces with noncompact boundaries. The main result is as follows: Let \(M_1\) and \(M_2\) be disjoint, properly embedded, stable minimal surfaces with noncompact boundaries in a complete flat 3-manifold. Then \(\text{dist}(M_1,M_2)=\min(\text{dist}(\partial M_1,M_2),\text{dist}(M_1,\partial M_2))\). If the boundary of one surface, say \(M_1\), is empty, then \(\text{dist}(M_1,M_2)= \text{dist}(M_1,\partial M_2)\).
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 780909
zbMATH Keywords: maximum principle at infinity
zbMATH Keywords: minimal surfaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 780909