Complex geodesics and complex Monge--Ampère equations with boundary singularity II
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866909428628848640 |
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| author | Wang, Xieping |
| author_facet | Wang, Xieping |
| contents | We study the parameter dependence of complex geodesics with prescribed boundary value and direction on bounded strongly linearly convex domains. As an important application we establish a quantitative relationship between the regularity of the pluricomplex Poisson kernel of such a domain, which is a solution to a homogeneous complex Monge--Ampère equation with boundary singularity, and the regularity of the boundary of the domain. Our results greatly improve the previous results of Chang--Hu--Lee and Bracci--Patrizio in this direction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_11988 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Complex geodesics and complex Monge--Ampère equations with boundary singularity II Wang, Xieping Complex Variables Analysis of PDEs Primary 32F45, 32W20, 32U35, Secondary 32F17, 35J96, 35B30 We study the parameter dependence of complex geodesics with prescribed boundary value and direction on bounded strongly linearly convex domains. As an important application we establish a quantitative relationship between the regularity of the pluricomplex Poisson kernel of such a domain, which is a solution to a homogeneous complex Monge--Ampère equation with boundary singularity, and the regularity of the boundary of the domain. Our results greatly improve the previous results of Chang--Hu--Lee and Bracci--Patrizio in this direction. |
| title | Complex geodesics and complex Monge--Ampère equations with boundary singularity II |
| topic | Complex Variables Analysis of PDEs Primary 32F45, 32W20, 32U35, Secondary 32F17, 35J96, 35B30 |
| url | https://arxiv.org/abs/2104.11988 |