Asymptotic Plateau problem for prescribed mean curvature hypersurfaces

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Casteras , J-B , Holopainen , I & Ripoll , J B 2020 , ' Asymptotic Plateau problem for prescribed mean curvature hypersurfaces ' , Proceedings of the American Mathematical Society , vol. 148 , no. 4 , pp. 1731-1743 . https://doi.org/10.1090/proc/14829

Title: Asymptotic Plateau problem for prescribed mean curvature hypersurfaces
Author: Casteras, Jean-Baptiste; Holopainen, Ilkka; Ripoll, Jaime B.
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Geometric Analysis and Partial Differential Equations
Date: 2020-04
Language: eng
Number of pages: 13
Belongs to series: Proceedings of the American Mathematical Society
ISSN: 1088-6826
URI: http://hdl.handle.net/10138/312449
Abstract: We prove the existence of solutions to the asymptotic Plateau problem for hypersurfaces of prescribed mean curvature in Cartan-Hadamard manifolds N. More precisely, given a suitable subset L of the asymptotic boundary of N and a suitable function H on N, we are able to construct a set of locally finite perimeter whose boundary has generalized mean curvature H provided that N satisfies the so-called strict convexity condition and that its sectional curvatures are bounded from above by a negative constant. We also obtain a multiplicity result in low dimensions.
Subject: 111 Mathematics
Hadamard manifolds
asymptotic Plateau problem
HADAMARD MANIFOLDS
EXISTENCE
REGULARITY
DIRICHLET
SURFACES
INFINITY
BOUNDARY
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