Existence and non-existence of minimal graphic and p-harmonic functions

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http://hdl.handle.net/10138/312016

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Casteras , J-B , Heinonen , E & Holopainen , I 2020 , ' Existence and non-existence of minimal graphic and p-harmonic functions ' , Proceedings of the Royal Society of Edinburgh. Section A, Mathematics , vol. 150 , no. 1 , 0308210518001348 , pp. 341-366 . https://doi.org/10.1017/prm.2018.134

Title: Existence and non-existence of minimal graphic and p-harmonic functions
Author: Casteras, Jean-Baptiste; Heinonen, Esko; Holopainen, Ilkka
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Geometric Analysis and Partial Differential Equations
Date: 2020-02-01
Language: eng
Number of pages: 26
Belongs to series: Proceedings of the Royal Society of Edinburgh. Section A, Mathematics
ISSN: 0308-2105
URI: http://hdl.handle.net/10138/312016
Abstract: We prove that every entire solution of the minimal graph equation that is bounded from below and has at most linear growth must be constant on a complete Riemannian manifold M with only one end if M has asymptotically non-negative sectional curvature. On the other hand, we prove the existence of bounded non-constant minimal graphic and p-harmonic functions on rotationally symmetric Cartan-Hadamard manifolds under optimal assumptions on the sectional curvatures.
Subject: 111 Mathematics
Mean curvature equation
p-Laplace equation
Dirichlet problem
Hadamard manifold
ASYMPTOTIC DIRICHLET PROBLEM
MEAN-CURVATURE
GREENS-FUNCTIONS
MANIFOLDS
THEOREMS
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