Brownian motion with respect to time-changing Riemannian metrics, applications to Ricci flow

Details Brownian motion with respect to time-changing Riemannian metrics, applications to Ricci flow Brownian motion with respect to time-changing Riemannian metrics, applications to Ricci flow

2009-01-14

arxiv.org/abs/0901.1999v2

Mathematics

Probability

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Brownian motion with respect to time-changing Riemannian metrics, applications to Ricci flow does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Brownian motion with respect to time-changing Riemannian metrics, applications to Ricci flow, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Brownian motion with respect to time-changing Riemannian metrics, applications to Ricci flow will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-375540