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Computing harmonic maps between Riemannian manifolds

Abstract : In [GLM18], 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.
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Preprints, Working Papers, ...
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Contributor : Brice Loustau Connect in order to contact the contributor
Submitted on : Saturday, October 19, 2019 - 10:20:37 PM
Last modification on : Wednesday, November 3, 2021 - 4:46:43 AM
Long-term archiving on: : Monday, January 20, 2020 - 1:44:33 PM


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  • HAL Id : hal-02320952, version 1



Jonah Gaster, Brice Loustau, Leonard Monsaingeon. Computing harmonic maps between Riemannian manifolds. 2019. ⟨hal-02320952⟩



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