Hölder estimates for degenerate complex Monge-Ampère equations
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911127954259968 |
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| author | Guo, Bin Kolodziej, Slawomir Song, Jian Sturm, Jacob |
| author_facet | Guo, Bin Kolodziej, Slawomir Song, Jian Sturm, Jacob |
| contents | Uniform $L^\infty$ and Hölder estimates were proved by the Kolodziej for complex Monge-Ampère equations on compact Kähler manifolds with $L^p$ volume measure with $p>1$. On the other hand, establishing Hölder estimates on singular Kähler varieties has remained open. In this paper, we establish uniform Hölder continuity for a family of complex Monge-Ampère equations on Kähler varieties, by developing a geometric regularization based on the partial $C^0$ estimate, i.e., quantitive Kodaira embeddings. As an application, we prove that local potentials of smoothable Kähler-Einstein varieties are Hölder continuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hölder estimates for degenerate complex Monge-Ampère equations Guo, Bin Kolodziej, Slawomir Song, Jian Sturm, Jacob Complex Variables Differential Geometry 53C55 Uniform $L^\infty$ and Hölder estimates were proved by the Kolodziej for complex Monge-Ampère equations on compact Kähler manifolds with $L^p$ volume measure with $p>1$. On the other hand, establishing Hölder estimates on singular Kähler varieties has remained open. In this paper, we establish uniform Hölder continuity for a family of complex Monge-Ampère equations on Kähler varieties, by developing a geometric regularization based on the partial $C^0$ estimate, i.e., quantitive Kodaira embeddings. As an application, we prove that local potentials of smoothable Kähler-Einstein varieties are Hölder continuous. |
| title | Hölder estimates for degenerate complex Monge-Ampère equations |
| topic | Complex Variables Differential Geometry 53C55 |
| url | https://arxiv.org/abs/2508.20933 |