Intrinsic Lipschitz maps vs. Lagrangian type solutions in Carnot groups of step 2

2021/08/04 by Di Donato, Daniela
#Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2108.02298

Abstract

We focus our attention on the notion of intrinsic Lipschitz graphs, inside a subclass of Carnot groups of step 2 which includes a corank 1 Carnot groups (and so the Heisenberg groups), Free groups of step 2 and the complexified Heisenberg group. More precisely, we prove the equivalence between intrinsic Lipschitz map and a weak solution to a suitable non linear first order PDE system, which generalizes Lagrangian solution in the context of Heisenberg groups.

Related

• Intrinsic Lipschitz graphs in Carnot groups of step 2
• Intrinsic Lipschitz sections of no-linear quotient maps
• Intrinsically Lipschitz graphs on semidirect products of groups
• Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups Hⁿ, n>1
• Intrinsic Lipschitz graphs and vertical β-numbers in the Heisenberg group