Exit Time Moments and Eigenvalue Estimates
We give upper bounds on the principal Dirichlet eigenvalue associated to a smoothly bounded domain in a complete Riemannian manifold; the bounds involve L1L1‐norms of exit time moments of Brownian motion. Our results generalize a classical inequality of Pólya. We also prove lower bounds for Dirichlet eigenvalues using invariants that arise during the examination of the relationship between the heat content and exit time moments.
Bulletin of the London Mathematical Society
Langford, Jeffrey J.; Dryden, Emily; and McDonald, Patrick. "Exit Time Moments and Eigenvalue Estimates." Bulletin of the London Mathematical Society (2017) : 480-490.