Sobolev-to-Lipschitz Property on QCD-spaces and Applications
Metric Geometry
2022-03-25 v2 Functional Analysis
Abstract
We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature dimension condition recently introduced in E. Milman, The Quasi Curvature-Dimension Condition with applications to sub-Riemannian manifolds, Comm. Pure Appl. Math. (to appear, arXiv:1908.01513v5). 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 result apply in particular to large classes of (ideal) sub-Riemannian manifolds.
Keywords
Cite
@article{arxiv.2110.05137,
title = {Sobolev-to-Lipschitz Property on QCD-spaces and Applications},
author = {Lorenzo Dello Schiavo and Kohei Suzuki},
journal= {arXiv preprint arXiv:2110.05137},
year = {2022}
}
Comments
17 pages, to appear in Math. Ann