Minimal Surfaces Over Carnot Manifolds Full article
| Journal |
Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126 |
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| Output data | Year: 2022, Volume: 32, Number: 3, Pages: 211-228 Pages count : 18 DOI: 10.1134/s105513442203004x | ||
| Tags | area functional; Carnot manifold; Carnot–Carathéodory space; graph-mapping; horizontal homomorphism; intrinsic measure; minimal surface; nilpotent graded group; sub-Riemannian mean curvature | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0006 |
Abstract:
We consider minimal graph-surfaces constructed from contact mappings of Carnot manifolds with values in Carnot–Caratheodory spaces. We establish basic properties of these graph-surfaces and distinguish the case in which the image space is endowed with the structure of a group. It turns out that, in the non-holonomic case, the problem is well posed if certain requirements on the preimage are satisfied. We find these requirements. One of auxiliary results provides us with an explicit form of the area formula for the graph constructed from a contact mapping.
Cite:
Karmanova M.B.
Minimal Surfaces Over Carnot Manifolds
Siberian Advances in Mathematics. 2022. V.32. N3. P.211-228. DOI: 10.1134/s105513442203004x Scopus РИНЦ OpenAlex
Minimal Surfaces Over Carnot Manifolds
Siberian Advances in Mathematics. 2022. V.32. N3. P.211-228. DOI: 10.1134/s105513442203004x Scopus РИНЦ OpenAlex
Original:
Карманова М.Б.
О минимальных поверхностях над многообразиями Карно произвольной глубины
Математические труды. 2022. Т.25. №1. С.74-101. DOI: 10.33048/mattrudy.2022.25.104 РИНЦ
О минимальных поверхностях над многообразиями Карно произвольной глубины
Математические труды. 2022. Т.25. №1. С.74-101. DOI: 10.33048/mattrudy.2022.25.104 РИНЦ
Identifiers:
| Scopus: | 2-s2.0-85137826864 |
| Elibrary: | 51556228 |
| OpenAlex: | W4294335264 |
Citing:
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