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Weak metrics on Euclidean domains

Athanase Papadopoulos·Marc Troyanov
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Abstract

A weak metric on a set is a function that satisfies the axioms of a metric except the symmetry and the separation axioms. In the present paper we introduced a weak metric, called the Apollonian weak metric, on any subset of a Euclidean space which is either bounded or whose boundary is unbounded. We then relate this weak metric to some familiar metrics such as the Poincare metric, the Klein-Hilbert metric, Funk metric, and the part metric which play an important role in classic and recent work on geometric function theory.

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Athanase Papadopoulos, Marc Troyanov. 2006-09-08. Weak metrics on Euclidean domains. https://arxiv.org/abs/math/0609236

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