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Minimal Surfaces Over Carnot Manifolds Научная публикация

Журнал

Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126

Вых. Данные

Год: 2022, Том: 32, Номер: 3, Страницы: 211-228 Страниц : 18 DOI: 10.1134/s105513442203004x

Ключевые слова

area functional; Carnot manifold; Carnot–Carathéodory space; graph-mapping; horizontal homomorphism; intrinsic measure; minimal surface; nilpotent graded group; sub-Riemannian mean curvature

Авторы

Karmanova M.B. ¹

Организации

1	Sobolev Institute of Mathematics, Novosibirsk, 630090 Russia

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0006

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.

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

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

Scopus:	2-s2.0-85137826864
РИНЦ:	51556228
OpenAlex:	W4294335264

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