Peak sections and Bergman kernels on Kähler manifolds with complex hyperbolic cusps
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909060425580544 |
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| author | Zhou, Shengxuan |
| author_facet | Zhou, Shengxuan |
| contents | By revisiting Tian's peak section method, we obtain a localization principle of the Bergman kernels on Kähler manifolds with complex hyperbolic cusps, which is a generalization of Auvray-Ma-Marinescu's localization result Bergman kernels on punctured Riemann surfaces [Auvray-Ma-Marinescu, Math. Ann., 2021]. Then we give some further estimates when the metric on the complex hyperbolic cusp is a Kähler-Einstein metric or when the manifold is a quotient of the complex ball. By applying our method directly to Poincaré type cusps, we also get a partial localization result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_04091 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Peak sections and Bergman kernels on Kähler manifolds with complex hyperbolic cusps Zhou, Shengxuan Complex Variables Differential Geometry By revisiting Tian's peak section method, we obtain a localization principle of the Bergman kernels on Kähler manifolds with complex hyperbolic cusps, which is a generalization of Auvray-Ma-Marinescu's localization result Bergman kernels on punctured Riemann surfaces [Auvray-Ma-Marinescu, Math. Ann., 2021]. Then we give some further estimates when the metric on the complex hyperbolic cusp is a Kähler-Einstein metric or when the manifold is a quotient of the complex ball. By applying our method directly to Poincaré type cusps, we also get a partial localization result. |
| title | Peak sections and Bergman kernels on Kähler manifolds with complex hyperbolic cusps |
| topic | Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2211.04091 |