Sharp conditions for preserving uniformity, doubling measure and Poincaré inequality under sphericalization
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915088088170496 |
|---|---|
| author | Korte, Riikka Rogovin, Sari Shanmugalingam, Nageswari Takala, Timo |
| author_facet | Korte, Riikka Rogovin, Sari Shanmugalingam, Nageswari Takala, Timo |
| contents | We study sphericalization, which is a mapping that conformally deforms the metric and the measure of an unbounded metric measure space so that the deformed space is bounded. The goal of this paper is to study sharp conditions on the deforming density function under which the sphericalization preserves uniformity of the space, the doubling property of the measure and the support of a Poincaré inequality. We also provide examples that demonstrate the sharpness of our conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01348 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp conditions for preserving uniformity, doubling measure and Poincaré inequality under sphericalization Korte, Riikka Rogovin, Sari Shanmugalingam, Nageswari Takala, Timo Metric Geometry We study sphericalization, which is a mapping that conformally deforms the metric and the measure of an unbounded metric measure space so that the deformed space is bounded. The goal of this paper is to study sharp conditions on the deforming density function under which the sphericalization preserves uniformity of the space, the doubling property of the measure and the support of a Poincaré inequality. We also provide examples that demonstrate the sharpness of our conditions. |
| title | Sharp conditions for preserving uniformity, doubling measure and Poincaré inequality under sphericalization |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2501.01348 |