Uniform diameter estimates for Kaehler metrics in big cohomology classes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913568881901568 |
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| author | Nguyen, Duc-Bao Vu, Duc-Viet |
| author_facet | Nguyen, Duc-Bao Vu, Duc-Viet |
| contents | We generalize previous diameter estimates and local non-vanishing of volumes for Kaehler metrics to the case of big cohomology classes. In our proof, among other things, we will prove a uniform diameter estimate for a family of smooth Kaehler metrics only involving an integrability condition. We also have to use fine stability properties of complex Monge-Ampere equations with prescribed singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18532 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform diameter estimates for Kaehler metrics in big cohomology classes Nguyen, Duc-Bao Vu, Duc-Viet Differential Geometry Complex Variables Metric Geometry We generalize previous diameter estimates and local non-vanishing of volumes for Kaehler metrics to the case of big cohomology classes. In our proof, among other things, we will prove a uniform diameter estimate for a family of smooth Kaehler metrics only involving an integrability condition. We also have to use fine stability properties of complex Monge-Ampere equations with prescribed singularities. |
| title | Uniform diameter estimates for Kaehler metrics in big cohomology classes |
| topic | Differential Geometry Complex Variables Metric Geometry |
| url | https://arxiv.org/abs/2410.18532 |