Simplicial energy and simplicial harmonic maps
Joel Hass, Peter Scott
TL;DR
This paper introduces a combinatorial energy for triangulated surface maps, analyzing harmonic maps' existence and uniqueness, and demonstrating applications similar to smooth harmonic maps.
Contribution
It presents a novel combinatorial energy framework for simplicial harmonic maps, extending smooth harmonic map concepts to triangulated surfaces.
Findings
Existence of simplicial harmonic maps established
Uniqueness properties analyzed
Applications analogous to smooth harmonic maps demonstrated
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.
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