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arXiv · 1306.6355

The Lusin theorem and horizontal graphs in the Heisenberg group

Piotr Hajlasz·Jacob Mirra
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Abstract

In this paper we prove that every collection of measurable functions $f_α$, $|α|=m$ coincides a.e. with $m$th order derivatives of a function $g\in C^{m-1}$ whose derivatives of order $m-1$ may have any modulus of continuity weaker than that of a Lipschitz function. This is a stronger version of earlier results of Lusin, Moonens-Pfeffer and Francos. As an application we construct surfaces in the Heisenberg group with tangent spaces being horizontal a.e.

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Piotr Hajlasz, Jacob Mirra. 2013-06-26. The Lusin theorem and horizontal graphs in the Heisenberg group. https://arxiv.org/abs/1306.6355

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