### Abstract

Let D be a simply connected domain on the complex plane such that 0 ∈ D. For r > 0, let D_{r} be the connected component of D ∩ z: |z| < r containing the origin. For fixed r, we solve the problem on minimization of the conformal radius R(D_{r}, 0) among all domains D with given conformal radius R(D, 0). This also leads to the solution of the problem on maximization of the logarithmic capacity of the local ε-extension E_{ε}(a) of E among all continua E with given logarithmic capacity. Here, E_{ε}(a) = E ∪ z: |z-a| ≤ ε, α ∈ E, ε > 0.

Original language | English |
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Article number | 341655 |

Pages (from-to) | 2220-2234 |

Number of pages | 15 |

Journal | Journal of Mathematical Sciences |

Volume | 105 |

Issue number | 4 |

DOIs | |

State | Published - 2001 |

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## Cite this

Solynin, A. Y. (2001). Minimization of the conformal radius under circular cutting of a domain.

*Journal of Mathematical Sciences*,*105*(4), 2220-2234. [341655]. https://doi.org/10.1023/A:1011337310404