Continuity of solutions to complex Monge-Ampère equations on compact Kähler spaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915445012955136 |
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| author | Cho, Ye-Won Luke Choi, Young-Jun |
| author_facet | Cho, Ye-Won Luke Choi, Young-Jun |
| contents | We prove the continuity of bounded solutions to complex Monge-Ampère equations on reduced, locally irreducible compact Kähler spaces. This in particular implies that any singular Kähler-Einstein potentials constructed in \cite{EGZ09} and \cite{Tsuji88, TianZhang06, ST17} are continuous. We also provide an affirmative answer to a conjecture in \cite{EGZ09} by showing that a resolution of any compact normal Kähler space satisfies the continuous approximation property. Finally, we settle the continuity of the potentials of the weak Kähler-Ricci flows \cite{ST17, GLZ20} on compact Kähler varieties with log terminal singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03935 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Continuity of solutions to complex Monge-Ampère equations on compact Kähler spaces Cho, Ye-Won Luke Choi, Young-Jun Differential Geometry Algebraic Geometry Complex Variables 14J17, 32Q20, 32U20, 32W20 We prove the continuity of bounded solutions to complex Monge-Ampère equations on reduced, locally irreducible compact Kähler spaces. This in particular implies that any singular Kähler-Einstein potentials constructed in \cite{EGZ09} and \cite{Tsuji88, TianZhang06, ST17} are continuous. We also provide an affirmative answer to a conjecture in \cite{EGZ09} by showing that a resolution of any compact normal Kähler space satisfies the continuous approximation property. Finally, we settle the continuity of the potentials of the weak Kähler-Ricci flows \cite{ST17, GLZ20} on compact Kähler varieties with log terminal singularities. |
| title | Continuity of solutions to complex Monge-Ampère equations on compact Kähler spaces |
| topic | Differential Geometry Algebraic Geometry Complex Variables 14J17, 32Q20, 32U20, 32W20 |
| url | https://arxiv.org/abs/2401.03935 |