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On $L^\infty$
estimates for Monge–Ampère and Hessian equations on nef
classes
Bin Guo, Duong H. Phong, Freid Tong and Chuwen Wang |
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Vol. 17 (2024), No. 2, 749–756
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Abstract |
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The PDE approach developed earlier by the first three authors for estimates for fully nonlinear equations on Kähler manifolds is shown to apply as well to Monge–Ampère and Hessian equations on nef classes. In particular, one obtains a new proof of the estimates of Boucksom, Eyssidieux, Guedj and Zeriahi (2010) and Fu, Guo and Song (2020) for the Monge–Ampère equation, together with their generalization to Hessian equations. |
Keywords
Monge–Ampere equations, Hessian equations
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Mathematical Subject Classification
Primary: 53C56
Secondary: 34G20
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Milestones
Received: 3 December 2021
Revised: 27 June 2022
Accepted: 26 July 2022
Published: 6 March 2024
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Authors |
| Bin Guo | |
| Department of Mathematics &
Computer Science Rutgers University Newark, NJ United States |
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| Duong H. Phong | |
| Department of Mathematics Columbia University New York, NY United States |
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| Freid Tong | |
| Center for Mathematical Sciences and
Applications Harvard University Cambridge, MA United States |
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| Chuwen Wang | |
| Department of Mathematics Columbia University New York, NY United States |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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