Local lower bounds on heat kernels

We analyze convolution semigroups on a regular measure space which satisfies the local doubling property. We assume the kernels are bounded and symmetric with the characteristic small-time, volume-dependent, singularity. Then, using a weak conservation property, we deduce local lower bounds with a comparable singularity. Applications are given to a wide range of subelliptic and strongly elliptic self-adjoint, or near self-adjoint, operators on Lie groups.