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Computing discrete equivariant harmonic maps

Abstract : We present effective methods to compute equivariant harmonic maps from the universal cover of a surface into a nonpositively curved space. By discretizing the theory appropriately, we show that the energy functional is strongly convex and derive convergence of the discrete heat flow to the energy minimizer, with explicit convergence rate. We also examine center of mass methods, after showing a generalized mean value property for harmonic maps. We feature a concrete illustration of these methods with Harmony, a computer software that we developed in C++, whose main functionality is to numerically compute and display equivariant harmonic maps.
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Contributor : Brice Loustau Connect in order to contact the contributor
Submitted on : Wednesday, May 15, 2019 - 11:38:45 PM
Last modification on : Wednesday, September 7, 2022 - 3:36:04 PM


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  • HAL Id : hal-02054982, version 2



Jonah Gaster, Brice Loustau, Leonard Monsaingeon. Computing discrete equivariant harmonic maps. 2019. ⟨hal-02054982v2⟩



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