Some variational problems for the complex Monge--Amp{è}re operator
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908965149868032 |
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| author | Chu, Jianchun Liu, Yaxiong McCleerey, Nicholas Zhang, Weijun |
| author_facet | Chu, Jianchun Liu, Yaxiong McCleerey, Nicholas Zhang, Weijun |
| contents | We consider the Dirichlet problem for the complex Monge--Ampère equation on strongly pseudoconvex Kähler manifolds when the right-hand side is decreasing in the solution. Using flow-based arguments, we establish existence of smooth solutions in a number of natural circumstances, following work of Chou-Wang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13421 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some variational problems for the complex Monge--Amp{è}re operator Chu, Jianchun Liu, Yaxiong McCleerey, Nicholas Zhang, Weijun Complex Variables Analysis of PDEs Differential Geometry 32W20, 35J20 We consider the Dirichlet problem for the complex Monge--Ampère equation on strongly pseudoconvex Kähler manifolds when the right-hand side is decreasing in the solution. Using flow-based arguments, we establish existence of smooth solutions in a number of natural circumstances, following work of Chou-Wang. |
| title | Some variational problems for the complex Monge--Amp{è}re operator |
| topic | Complex Variables Analysis of PDEs Differential Geometry 32W20, 35J20 |
| url | https://arxiv.org/abs/2604.13421 |