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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.21468 |
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| _version_ | 1866914057180676096 |
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| author | Rashmita Mukherjee, Sabyasachi |
| author_facet | Rashmita Mukherjee, Sabyasachi |
| contents | We prove a linear upper bound for the number of singular points on the boundary of a quadrature domain, improving a previously known quadratic bound due to Gustafsson \cite{Gus88}. This linear upper bound on the number of boundary double points also strengthens the bound on the connectivity (i.e., the number of complementary components) of a quadrature domain given by Lee and Makarov \cite{LM16}. Our proofs use conformal dynamics and hyperbolic geometry arguments. Finally, we introduce a new dynamical method to construct multiply connected quadrature domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On topology and singularities of quadrature domains Rashmita Mukherjee, Sabyasachi Complex Variables Dynamical Systems 30D05, 30E99, 30F10, 30F45, 37F31 (Primary), 30C20, 31A99 (Secondary) We prove a linear upper bound for the number of singular points on the boundary of a quadrature domain, improving a previously known quadratic bound due to Gustafsson \cite{Gus88}. This linear upper bound on the number of boundary double points also strengthens the bound on the connectivity (i.e., the number of complementary components) of a quadrature domain given by Lee and Makarov \cite{LM16}. Our proofs use conformal dynamics and hyperbolic geometry arguments. Finally, we introduce a new dynamical method to construct multiply connected quadrature domains. |
| title | On topology and singularities of quadrature domains |
| topic | Complex Variables Dynamical Systems 30D05, 30E99, 30F10, 30F45, 37F31 (Primary), 30C20, 31A99 (Secondary) |
| url | https://arxiv.org/abs/2509.21468 |