Computing harmonic maps between Riemannian manifolds
Abstract
In the previous paper [GLM2018], we showed that the theory of harmonic maps between Riemannian manifolds may be discretized by introducing triangulations with vertex and edge weights on the domain manifold. In the present paper, we study convergence of the discrete theory to the smooth theory when taking finer and finer triangulations. We present suitable conditions on the weighted triangulations that ensure convergence of discrete harmonic maps to smooth harmonic maps. Our computer software Harmony implements these methods to computes equivariant harmonic maps in the hyperbolic plane.
Cite
@article{arxiv.1910.08176,
title = {Computing harmonic maps between Riemannian manifolds},
author = {Jonah Gaster and Brice Loustau and Léonard Monsaingeon},
journal= {arXiv preprint arXiv:1910.08176},
year = {2020}
}
Comments
44 pages, 6 figures; v2 has substantially streamlined definition of almost asymptotically Laplacian (section 3.5), and constructions thereof (section 5), and added theorem statement in introduction