Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metric rectifiability of $\mathbb{H}$-regular surfaces with H\"older
  continuous horizontal normal   Two definitions for the rectfiability of hypersurfaces in Heisenberg groups
$\mathbb{H}^n$ have been proposed: one based on $\mathbb{H}$-regular surfaces,
and the other on Lipschitz images of subsets of codimension-$1$ vertical
subgroups. The equivalence between these notions remains an open problem.
Recent partial results are due to Cole-Pauls, Bigolin-Vittone, and Antonelli-Le
Donne.
  This paper makes progress in one direction: the metric Lipschitz
rectifiability of $\mathbb{H}$-regular surfaces. We prove that
$\mathbb{H}$-regular surfaces in $\mathbb{H}^{n}$ with $\alpha$-H\"older
continuous horizontal normal, $\alpha > 0$, are metric bilipschitz rectifiable.
This improves on the work by Antonelli-Le Donne, where the same conclusion was
obtained for $C^{\infty}$-surfaces.
  In $\mathbb{H}^{1}$, we prove a slightly stronger result: every
codimension-$1$ intrinsic Lipschitz graph with an $\epsilon$ of extra
regularity in the vertical direction is metric bilipschitz rectifiable. All the
proofs in the paper are based on a new general criterion for finding
bilipschitz maps between "big pieces" of metric spaces.

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The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
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The categories of this paper are: cs
34
The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int