The nonhomogeneous Cauchy-Riemann equation on families of open Riemann surfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911444158644224 |
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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 |