Polar Coordinates in Carnot groups II
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913813231566848 |
|---|---|
| author | Tyson, Jeremy T. |
| author_facet | Tyson, Jeremy T. |
| contents | A Carnot group is polarizable if it carries a homogeneous norm whose powers are fundamental solutions for the $p$-sub-Laplacian operators for all $1<p \le \infty$. Such groups also support a system of horizontal polar coordinates. We prove that the converse statement is true: if a Carnot group supports a horizontal polar coordinate system with suitable properties, then it is polarizable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_04913 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Polar Coordinates in Carnot groups II Tyson, Jeremy T. Analysis of PDEs Differential Geometry Metric Geometry 53C17 A Carnot group is polarizable if it carries a homogeneous norm whose powers are fundamental solutions for the $p$-sub-Laplacian operators for all $1<p \le \infty$. Such groups also support a system of horizontal polar coordinates. We prove that the converse statement is true: if a Carnot group supports a horizontal polar coordinate system with suitable properties, then it is polarizable. |
| title | Polar Coordinates in Carnot groups II |
| topic | Analysis of PDEs Differential Geometry Metric Geometry 53C17 |
| url | https://arxiv.org/abs/2208.04913 |