Calculus of Variations and Geometric Measure Theory

S. Nicolussi Golo - F. Serra Cassano

The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group

created by nicolussigolo on 14 Sep 2018



Inserted: 14 sep 2018
Last Updated: 14 sep 2018

Year: 2018

ArXiv: 1809.04586 PDF


We prove that, in the first Heisenberg group $\mathbb{H}$, an entire locally Lipschitz intrinsic graph admitting vanishing first variation of its sub-Riemannian area and non-negative second variation must be an intrinsic plane, i.e., a coset of a two dimensional subgroup of $\mathbb{H}$. Moreover two examples are given for stressing result's sharpness.