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arXiv · 1610.08873

A rough calculus approach to level sets in the Heisenberg group

Valentino Magnani·Eugene Stepanov·Dario Trevisan
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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.

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Valentino Magnani, Eugene Stepanov, Dario Trevisan. 2016-10-27. A rough calculus approach to level sets in the Heisenberg group. https://arxiv.org/abs/1610.08873

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