A1 Refereed original research article in a scientific journal

Conformally invariant complete metrics



Authors: Sugawa Toshiyuki, Vuorinen Matti, Zhang Tanran

Publisher: CAMBRIDGE UNIV PRESS

Publication year: 2023

Journal: Mathematical Proceedings of the Cambridge Philosophical Society

Journal name in source: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY

Journal acronym: MATH PROC CAMBRIDGE

Number of pages: 28

ISSN: 0305-0041

eISSN: 1469-8064

DOI: https://doi.org/10.1017/S030500412200024X

Web address : https://doi.org/10.1017/S030500412200024X

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/175747871

Preprint address: https://arxiv.org/abs/2009.06465v1


Abstract

For a domain G in the one-point compactification ¯Rn=Rn∪{∞} of Rn,n⩾2 , we characterise the completeness of the modulus metric μG in terms of a potential-theoretic thickness condition of ∂G, Martio’s M-condition [35]. Next, we prove that ∂G is uniformly perfect if and only if μG admits a minorant in terms of a Möbius invariant metric. Several applications to quasiconformal maps are given.


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Last updated on 2024-26-11 at 23:41