Weil-Petersson curves and Dirichlet finite harmonic functions on Riemann surfaces

Fuente: arXiv
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Autore principale: Matsuzaki, Katsuhiko
Natura: Preprint
Pubblicazione: 2025
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author Matsuzaki, Katsuhiko
author_facet Matsuzaki, Katsuhiko
contents On two subsurfaces of a Riemann surface divided by a $p$-Weil-Petersson curve $γ$, we consider the spaces of harmonic functions whose $p$-Dirichlet integrals are finite in the complementary domains of $γ$. By requiring the coincidence of boundary values on $γ$, we establish a correspondence between the harmonic functions in these Banach spaces. We analyze the operator arising from this correspondence via the composition operator acting on the Banach space of $p$-Besov functions on the unit circle.
format Preprint
id arxiv_https___arxiv_org_abs_2503_02377
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Weil-Petersson curves and Dirichlet finite harmonic functions on Riemann surfaces
Matsuzaki, Katsuhiko
Complex Variables
On two subsurfaces of a Riemann surface divided by a $p$-Weil-Petersson curve $γ$, we consider the spaces of harmonic functions whose $p$-Dirichlet integrals are finite in the complementary domains of $γ$. By requiring the coincidence of boundary values on $γ$, we establish a correspondence between the harmonic functions in these Banach spaces. We analyze the operator arising from this correspondence via the composition operator acting on the Banach space of $p$-Besov functions on the unit circle.
title Weil-Petersson curves and Dirichlet finite harmonic functions on Riemann surfaces
topic Complex Variables
url https://arxiv.org/abs/2503.02377