# Sobolev-to-Lipschitz Property on QCD-spaces and Applications

@inproceedings{Schiavo2021SobolevtoLipschitzPO, title={Sobolev-to-Lipschitz Property on QCD-spaces and Applications}, author={Lorenzo Dello Schiavo and Kohei Suzuki}, year={2021} }

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…

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