Simplicial energy and simplicial harmonic maps

Abstract

We introduce a combinatorial energy for maps of triangulated surfaces with simplicial metrics and analyze the existence and uniqueness properties of the corresponding harmonic maps. We show that some important applications of smooth harmonic maps can be obtained in this setting.

Version 1: 51 pages, 5 figures. Version 2: 52 pages, 6 figures. Several minor corrections, and some slightly modified statements and proofs in light of referee's comments. Version 3: 53 pages, 7 figures. Some further clarification added