Conformal Transformation of Uniform Domains Under Weights That Depend on Distance to The Boundary
The sphericalization procedure converts a Euclidean space into a compact sphere. In this note we propose a variant of this procedure for locally compact, rectifiably path-connected, non-complete, unbounded metric spaces by using conformal deformations that depend only on the distance to the boundary...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-09-01
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| Series: | Analysis and Geometry in Metric Spaces |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/agms-2022-0141 |
| _version_ | 1798014073850298368 |
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| author | Gibara Ryan Shanmugalingam Nageswari |
| author_facet | Gibara Ryan Shanmugalingam Nageswari |
| author_sort | Gibara Ryan |
| collection | DOAJ |
| description | The sphericalization procedure converts a Euclidean space into a compact sphere. In this note we propose a variant of this procedure for locally compact, rectifiably path-connected, non-complete, unbounded metric spaces by using conformal deformations that depend only on the distance to the boundary of the metric space. This deformation is locally bi-Lipschitz to the original domain near its boundary, but transforms the space into a bounded domain. We will show that if the original metric space is a uniform domain with respect to its completion, then the transformed space is also a uniform domain. |
| first_indexed | 2024-04-11T15:12:45Z |
| format | Article |
| id | doaj.art-6df378962c5d4157a9e9219708e2305f |
| institution | Directory Open Access Journal |
| issn | 2299-3274 |
| language | English |
| last_indexed | 2024-04-11T15:12:45Z |
| publishDate | 2022-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Analysis and Geometry in Metric Spaces |
| spelling | doaj.art-6df378962c5d4157a9e9219708e2305f2022-12-22T04:16:36ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742022-09-0110129731210.1515/agms-2022-0141Conformal Transformation of Uniform Domains Under Weights That Depend on Distance to The BoundaryGibara Ryan0Shanmugalingam Nageswari1Department of Mathematical Sciences, University of Cincinnati, Cincinnati, U.S.A.Department of Mathematical Sciences, University of Cincinnati, Cincinnati, U.S.A.The sphericalization procedure converts a Euclidean space into a compact sphere. In this note we propose a variant of this procedure for locally compact, rectifiably path-connected, non-complete, unbounded metric spaces by using conformal deformations that depend only on the distance to the boundary of the metric space. This deformation is locally bi-Lipschitz to the original domain near its boundary, but transforms the space into a bounded domain. We will show that if the original metric space is a uniform domain with respect to its completion, then the transformed space is also a uniform domain.https://doi.org/10.1515/agms-2022-0141uniform domainsconformal change in metricdistance to the boundaryprimary: 30l05secondary: 30l10 |
| spellingShingle | Gibara Ryan Shanmugalingam Nageswari Conformal Transformation of Uniform Domains Under Weights That Depend on Distance to The Boundary Analysis and Geometry in Metric Spaces uniform domains conformal change in metric distance to the boundary primary: 30l05 secondary: 30l10 |
| title | Conformal Transformation of Uniform Domains Under Weights That Depend on Distance to The Boundary |
| title_full | Conformal Transformation of Uniform Domains Under Weights That Depend on Distance to The Boundary |
| title_fullStr | Conformal Transformation of Uniform Domains Under Weights That Depend on Distance to The Boundary |
| title_full_unstemmed | Conformal Transformation of Uniform Domains Under Weights That Depend on Distance to The Boundary |
| title_short | Conformal Transformation of Uniform Domains Under Weights That Depend on Distance to The Boundary |
| title_sort | conformal transformation of uniform domains under weights that depend on distance to the boundary |
| topic | uniform domains conformal change in metric distance to the boundary primary: 30l05 secondary: 30l10 |
| url | https://doi.org/10.1515/agms-2022-0141 |
| work_keys_str_mv | AT gibararyan conformaltransformationofuniformdomainsunderweightsthatdependondistancetotheboundary AT shanmugalingamnageswari conformaltransformationofuniformdomainsunderweightsthatdependondistancetotheboundary |