Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A stochastic approach to the harmonic map heat flow on manifolds with
  time-dependent Riemannian metric   We first prove stochastic representation formulae for space-time harmonic
mappings defined on manifolds with evolving Riemannian metric. We then apply
these formulae to derive Liouville type theorems under appropriate curvature
conditions. Space-time harmonic mappings which are defined globally in time
correspond to ancient solutions to the harmonic map heat flow. As corollaries,
we establish triviality of such ancient solutions in a variety of different
situations.

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The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an