Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Brownian motion with respect to time-changing Riemannian metrics,
  applications to Ricci flow   We generalize Brownian motion on a Riemannian manifold to the case of a
family of metrics which depends on time. Such questions are natural for
equations like the heat equation with respect to time dependent Laplacians
(inhomogeneous diffusions). In this paper we are in particular interested in
the Ricci flow which provides an intrinsic family of time dependent metrics. We
give a notion of parallel transport along this Brownian motion, and establish a
generalization of the Dohrn-Guerra or damped parallel transport, Bismut
integration by part formulas, and gradient estimate formulas. One of our main
results is a characterization of the Ricci flow in terms of the damped parallel
transport. At the end of the paper we give an intrinsic definition of the
damped parallel transport in terms of stochastic flows, and derive an intrinsic
martingale which may provide information about singularities of the flow.

24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph