PARABOLIC HARNACK INEQUALITY ON METRIC SPACES WITH A GENERALIZED VOLUME PROPERTY

抄録

We study the parabolic Harnack inequality on metric measure spaces with the more general volume growth property than the volume doubling property. As applications we extend some Liouville theorems and heat kernel estimates for Riemannian manifolds to Alexandrov spaces satisfying a volume comparison condition of Bishop-Gromov type.