A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Intrinsic Geometry and Boundary Structure of Plane Domains
Tekijät: Rainio Oona, Sugawa Toshiyuki, Vuorinen Matti
Kustantaja: MAIK NAUKA/INTERPERIODICA/SPRINGER
Julkaisuvuosi: 2021
Journal: Siberian Mathematical Journal
Tietokannassa oleva lehden nimi: SIBERIAN MATHEMATICAL JOURNAL
Lehden akronyymi: SIBERIAN MATH J+
Vuosikerta: 62
Numero: 4
Aloitussivu: 691
Lopetussivu: 706
Sivujen määrä: 16
ISSN: 0037-4466
eISSN: 1573-9260
DOI: https://doi.org/10.1134/S0037446621040121
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/66954629
Given a nonempty compact set E in a proper subdomain Omega of the complex plane, we denote the diameter of E and the distance from E to the boundary of Omega by d(E) and d(E, partial derivative Omega), respectively. The quantity d(E)/d(E, partial derivative Omega) is invariant under similarities and plays an important role in geometric function theory. In case Omega has the hyperbolic distance h(Omega)(z, w), we consider the infimum kappa(Omega) of the quantity h(Omega)(E)/ log(1 + d(E)/d(E, partial derivative)) over compact subsets E of Omega with at least two points, where h(Omega)(E) stands for the hyperbolic diameter of E. Let the upper half-plane be H. We show that partial derivative(Omega) is positive if and only if the boundary of Omega is uniformly perfect and partial derivative(Omega) <= kappa(H) for all Omega, with equality holding precisely when Omega is convex.
Ladattava julkaisu This is an electronic reprint of the original article. |  |
