EVENT DETAILS AND ABSTRACT

Title: Brownian motion on open manifolds with big ends
Speaker: Jianguo Cao
Speaker Info: University of Notre Dame
Brief Description:
Special Note:
Abstract:

In this lecture, we will discuss the Brownian motion on non-compact manifolds with sufficiently large ends. We shall show that if such a manifold M satisfies a Gromov's length-area linear isoperimetric inequality then Brownian motion starting from any point in M converges almost surely to a point at infinity of M. Consequently, the Dirichlet problem at infinity is solvable for such an open space M.

No curvature assumption is needed in the above result, the open space M above is not necessarily to be diffeomorphic to the Euclidean space. For example, on any hyperbolic cone M over a (n-1)-dimensional space N, the Brownian motion starting from any point in M converges almost surely to a point at infinity.

This talk is accessible to all graduate students, no background of differential geometry is required.