Intrinsic metrics in polygonal domains

Dina Dautova, Rahim Kargar, Semen Nasyrov and Matti Vuorinen

Mathematische Nachrichten, 2023, vol. 296, issue 11, 4961-4977

Abstract: We study inequalities between the hyperbolic metric and intrinsic metrics in convex polygonal domains in the complex plane. A special attention is paid to the triangular ratio metric in rectangles. A local study leads to investigation of the relationship between the conformal radius at an arbitrary point of a planar domain and the distance of the point to the boundary.

Date: 2023
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https://doi.org/10.1002/mana.202200242

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