Title: Brownian motion on open manifolds with big ends
Speaker: Jianguo Cao
Speaker Info: University of Notre Dame
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.Date: Tuesday, March 27, 2001
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.