Calculus of Variations and Geometric Measure Theory
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S. Nicolussi Golo - F. Serra Cassano

The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group

created by nicolussigolo on 14 Sep 2018

[BibTeX]

preprint

Inserted: 14 sep 2018
Last Updated: 14 sep 2018

Year: 2018

ArXiv: 1809.04586 PDF

Abstract:

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.

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