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ID: 332750.0, MPI für Gravitationsphysik / Geometric Analysis and Gravitation
The $n$-dimensional analogue of the catenary: existence and nonexistence
Authors:Dierkes, Ulrich; Huisken, Gerhard
Date of Publication (YYYY-MM-DD):1990
Title of Journal:Pacific Journal of Mathematics
Journal Abbrev.:PJM
Volume:141
Issue / Number:1
Start Page:47
End Page:54
Review Status:not specified
Abstract / Description:We study "heavy" A?-dimensional surfaces suspended from some
prescribed (n — 1) -dimensional boundary data. This leads to a mean curvature type equation with a non-monotone right hand side. We show that the equation has no solution if the boundary data are too small, and, using a fixed point argument, that the problem always has a smooth solution for sufficiently large boundary data.
External Publication Status:published
Document Type:Article
Communicated by:Gerhard Huisken
Affiliations:MPI für Gravitationsphysik/Geometric Analysis and Gravitation
Identifiers:ISSN:0030-8730
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