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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2019 Number 5, Pages 15–29 (Mi ivm9460)

This article is cited in 7 papers

Minimal graph-surfaces on arbitrary two-step Carnot groups

M. B. Karmanova

Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, 4 Acad. Koptyug Ave., Novosibirsk, 630090 Russia

Abstract: We establish basic properties of minimal graph-surfaces constructed from classes of mappings defined on two-step Carnot groups. Research methods include solving of a specific question on correctness of the problem statement. A main result on necessary minimality conditions is formulated in terms of sub-Riemannian analog of mean curvature.

Keywords: two-step Carnot group, graph-mapping, minimal surface, mean curvature.

UDC: 517.2:517.4:514.7

Received: 26.03.2018
Revised: 17.07.2018
Accepted: 26.09.2018

DOI: 10.26907/0021-3446-2019-5-15-29


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:5, 13–26

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© Steklov Math. Inst. of RAS, 2025