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arXiv · 2508.13660

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

Franc Forstneric
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Abstract

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 H\"older 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.

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Franc Forstneric. 2025-08-19. The nonhomogeneous Cauchy-Riemann equation on families of open Riemann surfaces. https://doi.org/10.1007/s40627-025-00189-7

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