LOWER INEQUALITIES OF HEAT SEMIGROUPS BY USING PARABOLIC MAXIMUM PRINCIPLE

摘要

Using parabolic maximum principle, we apply the analytic method to obtain lower comparison inequalities for non-negative weak supersolutions of the heat equation associated with a regular strongly ρ-local Dirichlet form on the abstract metric measure space. As an application, we obtain lower estimates for heat kernels on some Riemannian manifolds.