On the convergence rate of Bergman metrics
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866929196924665856 |
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| author | Zhou, Shengxuan |
| author_facet | Zhou, Shengxuan |
| contents | We study the convergence rate of Bergman metrics on the class of polarized pointed Kähler $n$-manifolds $(M,L,g,x)$ with $\mathrm{Vol}\left( B_1 (x) \right) >v $ and $|\sec |\leq K $ on $M$. Relying on Tian's peak section method [Tian, 1990], we show that the $C^{1,α}$ convergence of Bergman metrics is uniform. At the end we discuss the sharpness of our estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_08883 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the convergence rate of Bergman metrics Zhou, Shengxuan Complex Variables Differential Geometry We study the convergence rate of Bergman metrics on the class of polarized pointed Kähler $n$-manifolds $(M,L,g,x)$ with $\mathrm{Vol}\left( B_1 (x) \right) >v $ and $|\sec |\leq K $ on $M$. Relying on Tian's peak section method [Tian, 1990], we show that the $C^{1,α}$ convergence of Bergman metrics is uniform. At the end we discuss the sharpness of our estimates. |
| title | On the convergence rate of Bergman metrics |
| topic | Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2112.08883 |