Intrinsic metrics in polygonal domains

Intrinsic metrics in polygonal domains

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...

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Veröffentlicht in:Mathematische Nachrichten 2023-11, Vol.296 (11), p.4961-4977
Hauptverfasser: Dautova, Dina, Kargar, Rahim, Nasyrov, Semen, Vuorinen, Matti
Format: Artikel
Sprache:eng
Schlagworte:
Polygons
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Zusammenfassung: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.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202200242