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

Katsuhiko Matsuzaki

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arXiv · 2503.02377

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

Katsuhiko Matsuzaki

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Abstract

On two subsurfaces of a Riemann surface divided by a $p$-Weil-Petersson curve $\gamma$, we consider the spaces of harmonic functions whose $p$-Dirichlet integrals are finite in the complementary domains of $\gamma$. By requiring the coincidence of boundary values on $\gamma$, 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.

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BibTeX RIS

Katsuhiko Matsuzaki. 2025-03-04. Weil-Petersson curves and Dirichlet finite harmonic functions on Riemann surfaces. https://arxiv.org/abs/2503.02377

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