Calculus of Variations and Geometric Measure Theory
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V. Magnani - E. Stepanov - D. Trevisan

A rough calculus approach to level sets in the Heisenberg group

created by magnani on 27 Oct 2016
modified on 28 Nov 2017

[BibTeX]

Submitted Paper

Inserted: 27 oct 2016
Last Updated: 28 nov 2017

Year: 2016

ArXiv: 1610.08873 PDF

Abstract:

We introduce novel equations, in the spirit of rough path theory, that parametrize level sets of intrinsically regular maps on the Heisenberg group with values in $\mathbb{R}^2$. These equations can be seen as a sub-Riemannian counterpart to classical ODEs arising from the implicit function theorem. We show that they enjoy all the natural well-posedness properties, thus allowing for a "good calculus" on nonsmooth level sets. We apply these results to prove an area formula for the intrinsic measure of level sets, along with the corresponding coarea formula.

Tags: GeMeThNES


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