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$C^{1,1}$ regularity
of degenerate complex Monge–Ampère equations and some
applications
Jianchun Chu |
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Vol. 14 (2021), No. 6, 1671–1700
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Abstract |
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We prove a estimate for solutions of complex Monge–Ampère equations on compact almost Hermitian manifolds. Using this estimate, we show the existence of solutions to the degenerate Monge–Ampère equations, the corresponding Dirichlet problems and the singular Monge–Ampère equations. We also study the singularities of the pluricomplex Green’s function. In addition, the proof of the above estimate is valid for a kind of complex Monge–Ampère-type equation. As a geometric application, we prove the regularity of geodesics in the space of Sasakian metrics. |
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Keywords
degenerate complex Monge–Ampère equation, $C^{1,1}$
estimate
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Mathematical Subject Classification 2010
Primary: 32W20
Secondary: 35J70, 53C15, 32Q60, 35J75, 53C25
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Milestones
Received: 12 December 2018
Revised: 30 March 2019
Accepted: 16 March 2020
Published: 7 September 2021
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Authors |
| Jianchun Chu | |
| Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China |
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