Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On minimal parabolic functions and time-homogeneous parabolic
  h-transforms   Does a minimal harmonic function $h$ remain minimal when it is viewed as a
parabolic function? The question is answered for a class of long thin
semi-infinite tubes $D\subset \R^d$ of variable width and minimal harmonic
functions $h$ corresponding to the boundary point of $D$ ``at infinity.''
Suppose $f(u)$ is the width of the tube $u$ units away from its endpoint and
$f$ is a Lipschitz function. The answer to the question is affirmative if and
only if $\int^\infty f^3(u)du = \infty$. If the test fails, there exist
parabolic $h$-transforms of space-time Brownian motion in $D$ with infinite
lifetime which are not time-homogenous.

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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
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The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph