Weil-Petersson curves and Dirichlet finite harmonic functions on Riemann surfaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918272485556224 |
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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 |