We propose a Dynkin-type condition for smooth Riemannian manifolds with boundary and show that this condition implies bi-Lipschitz equivalence with a Bakry-Émery weighted Riemannian manifold via a time change. As a consequence, we obtain various results, including a local doubling property as well as lower bounds on the Neumann spectral gap and logarithmic Sobolev constant. The local doubling property also yields a new precompactness theorem for manifolds with boundary.
The talk is based on joint work with David Tewodrose.
