On Kähler-Einstein Currents
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916613713821696 |
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| author | Chen, Yifan Chiu, Shih-Kai Hallgren, Max Székelyhidi, Gábor Tô, Tat Dat Tong, Freid |
| author_facet | Chen, Yifan Chiu, Shih-Kai Hallgren, Max Székelyhidi, Gábor Tô, Tat Dat Tong, Freid |
| contents | We show that a general class of singular Kähler metrics with Ricci curvature bounded below define Kähler currents. In particular the result applies to singular Kähler-Einstein metrics on klt pairs, and an analogous result holds for Kähler-Ricci solitons. In addition we show that if a singular Kähler-Einstein metric can be approximated by smooth metrics on a resolution whose Ricci curvature has negative part that is bounded uniformly in $L^p$ for $p > \frac{2n-1}{n}$, then the metric defines an RCD space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09825 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Kähler-Einstein Currents Chen, Yifan Chiu, Shih-Kai Hallgren, Max Székelyhidi, Gábor Tô, Tat Dat Tong, Freid Differential Geometry 53C25 We show that a general class of singular Kähler metrics with Ricci curvature bounded below define Kähler currents. In particular the result applies to singular Kähler-Einstein metrics on klt pairs, and an analogous result holds for Kähler-Ricci solitons. In addition we show that if a singular Kähler-Einstein metric can be approximated by smooth metrics on a resolution whose Ricci curvature has negative part that is bounded uniformly in $L^p$ for $p > \frac{2n-1}{n}$, then the metric defines an RCD space. |
| title | On Kähler-Einstein Currents |
| topic | Differential Geometry 53C25 |
| url | https://arxiv.org/abs/2502.09825 |