Conformally invariant complete metrics
| dc.contributor.author | Sugawa Toshiyuki | |
| dc.contributor.author | Vuorinen Matti | |
| dc.contributor.author | Zhang Tanran | |
| dc.contributor.organization | fi=matematiikka|en=Mathematics| | |
| dc.contributor.organization-code | 1.2.246.10.2458963.20.41687507875 | |
| dc.converis.publication-id | 175747871 | |
| dc.converis.url | https://research.utu.fi/converis/portal/Publication/175747871 | |
| dc.date.accessioned | 2022-10-28T12:44:29Z | |
| dc.date.available | 2022-10-28T12:44:29Z | |
| dc.description.abstract | <p>For a domain <em>G</em> in the one-point compactification ¯R<em>n</em>=R<em>n</em>∪{∞} of R<em>n</em>,<em>n</em>⩾2 , we characterise the completeness of the modulus metric <em>μ</em><em>G</em> in terms of a potential-theoretic thickness condition of ∂<em>G</em>, Martio’s <em>M</em>-condition [<strong><a href="https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/conformally-invariant-complete-metrics/17D6309D53B5787EAF16DFBF5F5011C8#r35">35</a></strong>]. Next, we prove that ∂<em>G</em> is uniformly perfect if and only if <em>μ</em><em>G</em> admits a minorant in terms of a Möbius invariant metric. Several applications to quasiconformal maps are given.</p> | |
| dc.identifier.eissn | 1469-8064 | |
| dc.identifier.jour-issn | 0305-0041 | |
| dc.identifier.olddbid | 178630 | |
| dc.identifier.oldhandle | 10024/161724 | |
| dc.identifier.uri | https://www.utupub.fi/handle/11111/36137 | |
| dc.identifier.url | https://doi.org/10.1017/S030500412200024X | |
| dc.identifier.urn | URN:NBN:fi-fe2022081154243 | |
| dc.language.iso | en | |
| dc.okm.affiliatedauthor | Vuorinen, Matti | |
| dc.okm.discipline | 111 Mathematics | en_GB |
| dc.okm.discipline | 111 Matematiikka | fi_FI |
| dc.okm.internationalcopublication | international co-publication | |
| dc.okm.internationality | International publication | |
| dc.okm.type | A1 ScientificArticle | |
| dc.publisher | CAMBRIDGE UNIV PRESS | |
| dc.publisher.country | United Kingdom | en_GB |
| dc.publisher.country | Britannia | fi_FI |
| dc.publisher.country-code | GB | |
| dc.relation.doi | 10.1017/S030500412200024X | |
| dc.relation.ispartofjournal | Mathematical Proceedings of the Cambridge Philosophical Society | |
| dc.source.identifier | https://www.utupub.fi/handle/10024/161724 | |
| dc.title | Conformally invariant complete metrics | |
| dc.year.issued | 2023 |
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