Sobolev-to-Lipschitz property on $${\mathsf {QCD}}$$-spaces and applications

Author:

Dello Schiavo LorenzoORCID,Suzuki KoheiORCID

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

Subject

General Mathematics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Harmonic functions and gravity localization;Journal of High Energy Physics;2023-09-20

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