Harmonic nets in metric spaces

Jürgen Jost and Leonard Todjihounde

Vol. 231 (2007), No. 2, 437–444

DOI: 10.2140/pjm.2007.231.437

Abstract

We investigate harmonic maps from weighted graphs into metric spaces that locally admit unique centers of gravity, like Alexandrov spaces with upper curvature bounds. We prove an existence result by constructing an iterative geometric process that converges to such maps, called harmonic nets for short.

Keywords

harmonic map, weighted graph, center of gravity, refinement

Mathematical Subject Classification 2000

Primary: 58E20, 53C43, 53C22

Milestones

Received: 7 July 2006

Accepted: 31 October 2006

Published: 1 June 2007