Abstract
AbstractWe prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds.
Funder
Japan Society for the Promotion of Science
Alexander von Humboldt-Stiftung
Austrian Science Fund
European Research Council
Publisher
Springer Science and Business Media LLC
Cited by
1 articles.
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1. Harmonic functions and gravity localization;Journal of High Energy Physics;2023-09-20