Preprints, Working Papers, ... Year : 2024

Computation of harmonic functions on higher genus surfaces

Abstract

We introduce a method to compute efficiently and with arbitrary precision a basis of harmonic functions with prescribed singularities on a general compact surface of genus two and more. This basis is obtained as a composition of theta functions and the Abel-Jacobi map, which is approximated at spectral speed by complex polynomials. We then implement this method to compute harmonic extensions on genus $2$ surfaces with boundary, that are described by their Fenchel-Nielsen coordinates and a smooth parametrization of the boundary. Finally, we prove the spectral convergence of the method for the harmonic extension.
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hal-04899536 , version 1 (20-01-2025)

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Mickaël Nahon, Edouard Oudet. Computation of harmonic functions on higher genus surfaces. 2024. ⟨hal-04899536⟩
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