On relative $L^\infty$ estimate for complex Monge-Ampère equations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909337289490432 |
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| author | Liu, Junbang |
| author_facet | Liu, Junbang |
| contents | We prove a relative $L^\infty$ estimate for a class of complex Monge-Ampère type equations on Kähler manifolds. It provides a unified approach to Tundinger type estimate and uniform estimate. It also improves the previous results about modulus of continuity, stability estimates, and $W^{1,1}$-estimates of Green's functions. The argument is based on the PDE method developed by Guo-Phong-Tong and constructing appropriate comparison metrics from entropy bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04393 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On relative $L^\infty$ estimate for complex Monge-Ampère equations Liu, Junbang Differential Geometry Analysis of PDEs We prove a relative $L^\infty$ estimate for a class of complex Monge-Ampère type equations on Kähler manifolds. It provides a unified approach to Tundinger type estimate and uniform estimate. It also improves the previous results about modulus of continuity, stability estimates, and $W^{1,1}$-estimates of Green's functions. The argument is based on the PDE method developed by Guo-Phong-Tong and constructing appropriate comparison metrics from entropy bound. |
| title | On relative $L^\infty$ estimate for complex Monge-Ampère equations |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2410.04393 |