Riemannian Polyhedra and Liouville-Type Theorems for Harmonic Maps

Riemannian Polyhedra and Liouville-Type Theorems for Harmonic Maps

This paper is a study of harmonic maps fromRiemannian polyhedra to locally non-positively curvedgeodesic spaces in the sense of Alexandrov. We prove Liouville-type theorems for subharmonic functionsand harmonic maps under two different assumptions on the source space. First we prove the analogue oft...

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Bibliographic Details
Main Author: Sinaei Zahra
Format: Article
Language:English
Published: De Gruyter 2014-01-01
Series:Analysis and Geometry in Metric Spaces
Subjects:
harmonic maps
riemannian polyhedra
pseudomanifolds
liouville-type theorem
non-negativericci
Online Access:https://doi.org/10.2478/agms-2014-0012
Description
Summary:This paper is a study of harmonic maps fromRiemannian polyhedra to locally non-positively curvedgeodesic spaces in the sense of Alexandrov. We prove Liouville-type theorems for subharmonic functionsand harmonic maps under two different assumptions on the source space. First we prove the analogue ofthe Schoen-Yau Theorem on a complete pseudomanifolds with non-negative Ricci curvature. Then we study2-parabolic admissible Riemannian polyhedra and prove some vanishing results on them.
ISSN:2299-3274

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