Riemannian Polyhedra and Liouville-type Theorems for Harmonic maps

Zahra Sinaei

Riemannian Polyhedra and Liouville-type Theorems for Harmonic maps

Metric Geometry 2014-12-02 v3

Authors: Zahra Sinaei

Abstract

This paper is a study of harmonic maps from Riemannian 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 (smooth) pseudomanifolds with non-negative Ricci curvature. Then we study 2-parabolic admissible Riemannian polyhedra and prove some vanishing results on them.

Keywords

riemannian polyhedra harmonic maps liouville-type theorems alexandrov spaces non-positive curvature schoen-yau theorem pseudomanifolds ricci curvature

Cite

@article{arxiv.1209.5889,
  title  = {Riemannian Polyhedra and Liouville-type Theorems for Harmonic maps},
  author = {Zahra Sinaei},
  journal= {arXiv preprint arXiv:1209.5889},
  year   = {2014}
}

Comments

References added. Minor typos fixed

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