On the $L^2$ volume of Bergman spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929320854814720 |
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| author | Zhou, Shengxuan |
| author_facet | Zhou, Shengxuan |
| contents | In this paper, we show that the Calabi volume and Mabuchi volume of Bergman spaces on the product of a projective manifold and a projective space is infinite. Our result is inspired by a conjecture of Shiffman-Zelditch in [arXiv:2303.11559]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12840 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $L^2$ volume of Bergman spaces Zhou, Shengxuan Complex Variables Differential Geometry In this paper, we show that the Calabi volume and Mabuchi volume of Bergman spaces on the product of a projective manifold and a projective space is infinite. Our result is inspired by a conjecture of Shiffman-Zelditch in [arXiv:2303.11559]. |
| title | On the $L^2$ volume of Bergman spaces |
| topic | Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2404.12840 |