Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The engulfing property for sections of convex functions in the
  Heisenberg group and the associated quasi--metric   In this paper we investigate the property of engulfing for $H$-convex
functions defined on the Heisenberg group ${\mathbb{H}}^n$. Starting from the
horizontal sections introduced by Capogna and Maldonado, we consider a new
notion of section, called ${\mathbb{H}}^n$-section, as well as a new condition
of engulfing associated to the ${\mathbb{H}}^n$-sections, for an $H$-convex
function defined in ${\mathbb{H}}^n.$ These sections, that arise as suitable
unions of horizontal sections, are dimensionally larger; as a matter of fact,
the ${\mathbb{H}}^n$-sections, with their engulfing property, will lead to the
definition of a pseudo-metric in ${\mathbb{H}}^n$ in a way similar to Aimar,
Forzani and Toledano in the Euclidean case. A key role is played by the
property of round $H$-sections for an $H$-convex function, and by its
connection with the engulfing properties.

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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin