This article is cited in 1 paper

Lipschitz graphs on classes of two-step Carnot groups

M. B. Karmanova

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We consider two-step Carnot groups and their model cases and study the existence of graph mappings on them that are Lipschitz in the intrinsic sense. For the general case of two-step Carnot groups, a criterion for the Lipschitz property of a graph mapping is derived in terms of the mapping that models this graph. Examples are given that demonstrate the specificity of the necessary and sufficient conditions established.

Keywords: Lipschitz mapping, intrinsic metric, graph mapping, two-step Carnot group.

UDC: 517.518

MSC: 35R30

Received: 26.03.2025
Revised: 26.03.2025
Accepted: 25.04.2025

DOI: 10.33048/smzh.2025.66.509

 English version: Siberian Mathematical Journal, 2025, 66:5, 1195–1211