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<p>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,&#xa0;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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月29日

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  • Franc Forstnerič

摘要

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.