The nonhomogeneous Cauchy-Riemann equation on families of open Riemann surfaces

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1. Verfasser: Forstneric, Franc
Format: Preprint
Veröffentlicht: 2025
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author Forstneric, Franc
author_facet Forstneric, Franc
contents In this paper we use the nonhomogeneous Beltrami equation to give an optimal solution to the nonhomogeneous Cauchy-Riemann equation for continuous or smooth families of complex structures and $(0,1)$-forms of a Hölder class on a smooth open orientable surface. As an application, we obtain the Oka-Grauert principle for complex line bundles on families of open Riemann surfaces.
format Preprint
id arxiv_https___arxiv_org_abs_2508_13660
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The nonhomogeneous Cauchy-Riemann equation on families of open Riemann surfaces
Forstneric, Franc
Complex Variables
Primary 32W05, secondary 32Q56, 32L20
In this paper we use the nonhomogeneous Beltrami equation to give an optimal solution to the nonhomogeneous Cauchy-Riemann equation for continuous or smooth families of complex structures and $(0,1)$-forms of a Hölder class on a smooth open orientable surface. As an application, we obtain the Oka-Grauert principle for complex line bundles on families of open Riemann surfaces.
title The nonhomogeneous Cauchy-Riemann equation on families of open Riemann surfaces
topic Complex Variables
Primary 32W05, secondary 32Q56, 32L20
url https://arxiv.org/abs/2508.13660