A Coarea Formula for Smooth Contact Mappings of Carnot–Carathéodory Spaces Full article
| Journal |
Acta Applicandae Mathematicae
ISSN: 0167-8019 , E-ISSN: 1572-9036 |
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| Output data | Year: 2013, Volume: 128, Number: 1, Pages: 67-111 Pages count : 45 DOI: 10.1007/s10440-013-9822-7 | ||
| Tags | Carnot manifold · Differentiability · Coarea formula · Level set | ||
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Abstract:
We prove the coarea formula for sufficiently smooth contact mappings of Carnot
manifolds to Carnot–Carathéodory spaces. In particular, we investigate level surfaces of
these mappings, and compare Riemannian and sub-Riemannian measures on them. Our
main tool is the sharp asymptotic behavior of the Riemannian measure of the intersection of
a tangent plane to a level surface and a sub-Riemannian ball. This calculation in particular
implies that the sub-Riemannian measure of the set of characteristic points (i.e., the points
at which the sub-Riemannian differential is degenerate) equals zero on almost every level
set.
Cite:
Karmanova M.
, Vodopyanov S.
A Coarea Formula for Smooth Contact Mappings of Carnot–Carathéodory Spaces
Acta Applicandae Mathematicae. 2013. V.128. N1. P.67-111. DOI: 10.1007/s10440-013-9822-7 WOS Scopus РИНЦ OpenAlex
A Coarea Formula for Smooth Contact Mappings of Carnot–Carathéodory Spaces
Acta Applicandae Mathematicae. 2013. V.128. N1. P.67-111. DOI: 10.1007/s10440-013-9822-7 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Oct 25, 2011 |
| Accepted: | Mar 15, 2026 |
| Published online: | Apr 11, 2026 |
Identifiers:
| ≡ Web of science: | WOS:000326802700004 |
| ≡ Scopus: | 2-s2.0-84888370050 |
| ≡ Elibrary: | 23971275 |
| ≡ OpenAlex: | W2007727155 |