---
_id: '10588'
abstract:
- lang: eng
text: We 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.
acknowledgement: "The authors are grateful to Dr. Bang-Xian Han for helpful discussions
on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor
Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino
Antonelli for reading a preliminary version of this work and for their valuable
comments and suggestions. Finally, they wish to express their gratitude to two anonymous
Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S.
gratefully acknowledges funding of his position by the Austrian Science Fund (FWF)
grant F65, and by the European Research Council (ERC, grant No. 716117, awarded
to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS
Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research
Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research
on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number
17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Kohei
full_name: Suzuki, Kohei
last_name: Suzuki
citation:
ama: Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and
applications. Mathematische Annalen. 2022;384:1815-1832. doi:10.1007/s00208-021-02331-2
apa: Dello Schiavo, L., & Suzuki, K. (2022). Sobolev-to-Lipschitz property on
QCD- spaces and applications. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-021-02331-2
chicago: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property
on QCD- Spaces and Applications.” Mathematische Annalen. Springer Nature,
2022. https://doi.org/10.1007/s00208-021-02331-2.
ieee: L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces
and applications,” Mathematische Annalen, vol. 384. Springer Nature, pp.
1815–1832, 2022.
ista: Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces
and applications. Mathematische Annalen. 384, 1815–1832.
mla: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on
QCD- Spaces and Applications.” Mathematische Annalen, vol. 384, Springer
Nature, 2022, pp. 1815–32, doi:10.1007/s00208-021-02331-2.
short: L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.
date_created: 2022-01-02T23:01:35Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2023-08-02T13:39:05Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00208-021-02331-2
ec_funded: 1
external_id:
arxiv:
- '2110.05137'
isi:
- '000734150200001'
file:
- access_level: open_access
checksum: 2593abbf195e38efa93b6006b1e90eb1
content_type: application/pdf
creator: alisjak
date_created: 2022-01-03T11:08:31Z
date_updated: 2022-01-03T11:08:31Z
file_id: '10596'
file_name: 2021_MathAnn_DelloSchiavo.pdf
file_size: 410090
relation: main_file
success: 1
file_date_updated: 2022-01-03T11:08:31Z
has_accepted_license: '1'
intvolume: ' 384'
isi: 1
keyword:
- quasi curvature-dimension condition
- sub-riemannian geometry
- Sobolev-to-Lipschitz property
- Varadhan short-time asymptotics
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 1815-1832
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Mathematische Annalen
publication_identifier:
eissn:
- 1432-1807
issn:
- 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sobolev-to-Lipschitz property on QCD- spaces and applications
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 384
year: '2022'
...