Some remarks on contact variations in the first Heisenberg group

2016/11/22 by Golo, Sebastiano · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.07358

Abstract

We show that in the first sub-Riemannian Heisenberg group there are intrinsic graphs of smooth functions that are both critical and stable points of the sub-Riemannian perimeter under compactly supported variations of contact diffeomorphisms, despite the fact that they are not area-minimizing surfaces. In particular, we show that if f:ℝ²→ℝ is a C¹-intrinsic function, and ∇^f∇^ff=0, then the first contact variation of the sub-Riemannian area of its intrinsic graph is zero and the second contact variation is positive.

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