Geometry of Carnot--Carathéodory Spaces, Differentiability and Coarea Formula
| dc.creator | Karmanova, Maria | |
| dc.creator | Vodopyanov, Sergey | |
| dc.date | 2008-04-21 | |
| dc.date | 2008-05-26 | |
| dc.date.accessioned | 2026-07-07T09:40:36Z | |
| dc.date.available | 2026-07-07T09:40:36Z | |
| dc.description | We give a simple proof of Gromov's Theorem on nilpotentization of vector fields, and exhibit a new method for obtaining quantitative estimates of comparing geometries of two different local Carnot groups in Carnot--Carathéodory spaces with $C^{1,α}$-smooth basis vector fields, $α\in[0,1]$. From here we obtain the similar estimates for comparing geometries of a Carnot--Carathéodory space and a local Carnot group. These two theorems imply basic results of the theory: Gromov type Local Approximation Theorems, and for $α>0$ Rashevski\vı-Chow Theorem and Ball--Box Theorem, etc. We apply the obtained results for proving $hc$-differentiability of mappings of Carnot--Carathéodory spaces with continuous horizontal derivatives. The latter is used in proving the coarea formula for some classes of contact mappings of Carnot--Carathéodory spaces. | |
| dc.description | 94 pages | |
| dc.identifier | https://arxiv.org/abs/0804.3291 | |
| dc.identifier | http://arxiv.org/abs/0804.3291 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161534 | |
| dc.subject | Metric Geometry | |
| dc.subject | 53C17, 28A75, 58C35, 93B29 | |
| dc.title | Geometry of Carnot--Carathéodory Spaces, Differentiability and Coarea Formula | |
| dc.type | text |