Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monge-Amp\`ere of Pac-Man   We show that the Monge-Amp\`ere density of the extremal function $V_P$ for a
non-convex Pac-Man set $P\subset {\bf R}^2$ tends to a finite limit as we
approach the vertex $p$ of $P$ linearly but with a value that may vary with the
line. On the other hand, along a tangential approach to $p$ the Monge-Amp\`ere
density becomes unbounded. This partially mimics the behavior of the
Monge-Amp\`ere density of the union of two quarter disks set $S$ of Sigurdsson
and Snaebjarnarson. We also recover their formula for $V_S$ by elementary
methods.

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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga