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Intrinsic metrics in polygonal domains

Complex Variables 2022-06-09 v1 Metric Geometry

Abstract

We study inequalities between the hyperbolic metric and intrinsic metrics in convex polygonal domains in the complex plane. Special attention is paid to the triangular ratio metric in rectangles. A local study leads to an 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.

Keywords

Cite

@article{arxiv.2206.03744,
  title  = {Intrinsic metrics in polygonal domains},
  author = {D. Dautova and R. Kargar and S. Nasyrov and M. Vuorinen},
  journal= {arXiv preprint arXiv:2206.03744},
  year   = {2022}
}

Comments

20 pages, 7 figures