Geometric analysis for Brownian motion on manifolds with non-standard boundary behaviourOberseminar Stochastics
by
Endenicher Allee 60/1-016 - Lipschitzsaal
Mathezentrum
We consider Brownian motion on manifolds with sticky reflection from the
boundary and with or without diffusion along the boundary. For the invariant
measure consisting of a convex combination of the volume measure in the
interior and the Hausdorff measure on the boundary we show upper bounds
on the Poincaré and logarithmic Sobolev constants under general curvature
assumptions on the manifold and its boundary. The proof is based on an interpolation involving energy interactions between the boundary and the interior
of the manifold. Additionally, we also present a Cheeger-type inequality to
bound the spectral gap from below. As a side result we obtain explicit geometric bounds on the first non-trivial Steklov eigenvalue.
The talk is based on joint work with Max von Renesse and Feng-Yu Wang.