Riemannian polyhedra and liouville-Type theorems for harmonic maps

Zahra Sinaei

doi:10.2478/agms-2014-0012

Riemannian polyhedra and liouville-Type theorems for harmonic maps

Zahra Sinaei^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

This paper is a study of harmonic maps fromRiemannian polyhedra to locally non-positively curved geodesic spaces in the sense of Alexandrov. We prove Liouville-Type theorems for subharmonic functions and harmonic maps under two different assumptions on the source space. First we prove the analogue of the Schoen-Yau Theorem on a complete pseudomanifolds with non-negative Ricci curvature. Then we study 2-parabolic admissible Riemannian polyhedra and prove some vanishing results on them.

Original language	English (US)
Pages (from-to)	294-318
Number of pages	25
Journal	Analysis and Geometry in Metric Spaces
Volume	2
Issue number	1
DOIs	https://doi.org/10.2478/agms-2014-0012
State	Published - 2014

Keywords

Harmonic maps
Liouville-Type theorem
Non-negative Ricci
Pseudomanifolds
Riemannian polyhedra

ASJC Scopus subject areas

Analysis
Geometry and Topology
Applied Mathematics

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AB - This paper is a study of harmonic maps fromRiemannian polyhedra to locally non-positively curved geodesic spaces in the sense of Alexandrov. We prove Liouville-Type theorems for subharmonic functions and harmonic maps under two different assumptions on the source space. First we prove the analogue of the Schoen-Yau Theorem on a complete pseudomanifolds with non-negative Ricci curvature. Then we study 2-parabolic admissible Riemannian polyhedra and prove some vanishing results on them.

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