Abstract:
We prove a sub-Riemannian analogue of the area formula for Lipschitz
mappings (in the sub-Riemannian sense) between equiregular
Carnot–Carathéodory spaces. In particular, we give an adequate
analytic definition of the sub-Riemannian Jacobian.
Keywords:
Carnot–Carathéodory space, differentiability, Lipschitz mapping,
sub-Riemannian quasi-metric, area formula.
\Bibitem{Kar14}
\by M.~B.~Karmanova
\paper An area formula for Lipschitz mappings of Carnot--Carath\'eodory spaces
\jour Izv. Math.
\yr 2014
\vol 78
\issue 3
\pages 475--499
\mathnet{http://mi.mathnet.ru/eng/im8083}
\crossref{https://doi.org/10.1070/IM2014v078n03ABEH002695}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3241818}
\zmath{https://zbmath.org/?q=an:06323421}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2014IzMat..78..475K}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000338994800004}
\elib{https://elibrary.ru/item.asp?id=21826418}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84903455827}
Linking options:
https://www.mathnet.ru/eng/im8083
https://doi.org/10.1070/IM2014v078n03ABEH002695
https://www.mathnet.ru/eng/im/v78/i3/p53
This publication is cited in the following 22 articles:
M. B. Karmanova, “The Area of Images of Classes of Measurable Sets on Carnot Groups with Sub-Lorentzian Structure”, Sib Math J, 65:5 (2024), 1116
M. B. Karmanova, “Ploschad obrazov klassov izmerimykh mnozhestv na gruppakh Karno s sublorentsevoi strukturoi”, Sib. matem. zhurn., 65:5 (2024), 926–952
M. B. Karmanova, “Metric characteristics of classes of compact sets on Carnot groups with sub-Lorentzian structure”, Vladikavk. matem. zhurn., 26:3 (2024), 56–64
M. B. Karmanova, “Measure of Images of Contact Mappings on Two-Step Sub-Lorentzian Structures”, Math. Notes, 113:1 (2023), 154–158
Marcela Garriga, Pablo Ochoa, “Area Formulas in Metric Measure Spaces Under a Weak Lipschitz-Like Condition”, Results Math, 78:1 (2023)
M. B. Karmanova, “The area of surfaces on sub-Lorentzian structures of depth two”, Siberian Adv. Math., 33:3 (2023), 214–229
M. B. Karmanova, “Lipschitz images of open sets on sub-Lorentzian structures”, Siberian Adv. Math., 34:1 (2024), 67–79
M. B. Karmanova, “O minimalnykh poverkhnostyakh nad mnogoobraziyami Karno proizvolnoi glubiny”, Matem. tr., 25:1 (2022), 74–101
M. B. Karmanova, “Minimal Surfaces Over Carnot Manifolds”, Sib. Adv. Math., 32:3 (2022), 211
M. B. Karmanova, “Properties of minimal surfaces over depth 2 Carnot manifolds”, Siberian Math. J., 62:6 (2021), 1050–1062
M. B. Karmanova, “Two-step sub-Lorentzian structures and graph surfaces”, Izv. Math., 84:1 (2020), 52–94
M. B. Karmanova, “The area of graphs on arbitrary carnot groups with sub-lorentzian structure”, Siberian Math. J., 61:4 (2020), 648–670
M. B. Karmanova, “Level sets of classes of mappings of two-step Carnot groups in a nonholonomic interpretation”, Siberian Math. J., 60:2 (2019), 304–311
M. B. Karmanova, “Area of graph surfaces on Carnot groups with sub-Lorentzian structure”, 99, no. 2, 2019, 145–148
M. B. Karmanova, “Local metric properties of level surfaces on Carnot-Caratheodory spaces”, Dokl. Math., 99:1 (2019), 75–78
M. B. Karmanova, “On the class of Hölder surfaces in Carnot–Carathéodory spaces”, Siberian Math. J., 60:5 (2019), 861–885
M. B. Karmanova, “On local metric characteristics of level sets of ch1-mappings of carnot manifolds”, Siberian Math. J., 60:6 (2019), 1007–1021
M. B. Karmanova, “Graph surfaces on five-dimensional sub-Lorentzian structures”, Siberian Math. J., 58:1 (2017), 91–108
M. B. Karmanova, “Metric properties of classes of Hölder surfaces on Carnot groups”, Dokl. Math., 95:2 (2017), 118–121
M. B. Karmanova, “Area formulas for classes of Hölder continuous mappings of Carnot groups”, Siberian Math. J., 58:5 (2017), 817–836
Citation in format AMSBIB
Contact us: