On the $$L^\infty $$ L ∞ -Uniqueness of Symmetric Diffusion Operators on Complete Non-Compact Riemannian Manifolds

Abstract

Using an interplay between the methods of geometric analysis and stochastic analysis, the main purpose of this paper is to study the \(L^\infty \)-uniqueness for symmetric diffusion operators on complete non-compact Riemannian manifolds in the context of \(m\)-dimensional Bakry–Emery’s Ricci curvature.