Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.25076 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908618729717760 |
|---|---|
| author | Zhang, Yanfang Zhang, Shu-Qin |
| author_facet | Zhang, Yanfang Zhang, Shu-Qin |
| contents | It is well known that if a metric space is uniformly disconnected, then its conformal dimension is zero. First, we characterize when a self-affine sponge of Lalley-Gatzouras type is uniformly disconnected. Thanks to this characterization, we show that a self-affine sponge of Lalley-Gatzouras type has conformal dimension zero if and only if it is uniformly disconnected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25076 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When the conformal dimension of a self-affine sponge of Lalley-Gatzouras type is zero Zhang, Yanfang Zhang, Shu-Qin Metric Geometry General Topology 26A16, 28A12, 28A80 It is well known that if a metric space is uniformly disconnected, then its conformal dimension is zero. First, we characterize when a self-affine sponge of Lalley-Gatzouras type is uniformly disconnected. Thanks to this characterization, we show that a self-affine sponge of Lalley-Gatzouras type has conformal dimension zero if and only if it is uniformly disconnected. |
| title | When the conformal dimension of a self-affine sponge of Lalley-Gatzouras type is zero |
| topic | Metric Geometry General Topology 26A16, 28A12, 28A80 |
| url | https://arxiv.org/abs/2510.25076 |