Pré-Publication, Document De Travail Année : 2024

Computation of harmonic functions on higher genus surfaces

Résumé

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.
Fichier principal
Vignette du fichier
HigherGenus_paper.pdf (8.49 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
licence
Copyright (Tous droits réservés)

Dates et versions

hal-04899536 , version 1 (20-01-2025)

Licence

Copyright (Tous droits réservés)

Identifiants

Citer

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

Altmetric

Partager

More