Spectral Gap Estimates for Brownian Motion on Manifolds with Sticky Reflecting Boundary Diffusion

We review some basic concepts in the interplay of Ricci curvature and Brownian motion on Riemannian manifolds. The second part is devoted to some new results for the case of sticky reflecting boundary diffusion. Such processes interpolate between plain Neumann reflection in the interior and surface diffusion on the boundary. We present new spectral gap estimates in terms of Ricci curvature in the interior and mean curvature on the boundary. (Joint work with Victor Marx and Vitalii Konarovskyi.)