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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.00609 |
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| _version_ | 1866914077246226432 |
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| author | Pan, Junyu |
| author_facet | Pan, Junyu |
| contents | In this paper, a simplified exposition of the celebrated Aubin-Yau proof for the existence of Kähler-Einstein metrics is provided. For the case of a compact Kähler manifold with vanishing first Chern class, the analysis presents an alternative formulation of the $C^0$ a priori estimate. Instead of relying on the $L^{\infty}$ norm of the Kähler potential $F$ as in the original proof, a different uniform bound for the solution to the Monge-Ampère equation that depends only on the $L^{p}$ norm of $e^{F}$ is established. This estimate has a stronger version established by Kołodziej in 1998. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00609 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Simplification of the Aubin-Yau Proof and an Alternative $C^{0}$ Estimate for the Monge-Ampère Equation on Calabi-Yau Manifolds Pan, Junyu Differential Geometry In this paper, a simplified exposition of the celebrated Aubin-Yau proof for the existence of Kähler-Einstein metrics is provided. For the case of a compact Kähler manifold with vanishing first Chern class, the analysis presents an alternative formulation of the $C^0$ a priori estimate. Instead of relying on the $L^{\infty}$ norm of the Kähler potential $F$ as in the original proof, a different uniform bound for the solution to the Monge-Ampère equation that depends only on the $L^{p}$ norm of $e^{F}$ is established. This estimate has a stronger version established by Kołodziej in 1998. |
| title | A Simplification of the Aubin-Yau Proof and an Alternative $C^{0}$ Estimate for the Monge-Ampère Equation on Calabi-Yau Manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.00609 |