Metric measure spaces and Ricci curvature — analytic, geometric, and probabilistic challenges

Project Information

RicciBounds

Grant agreement ID: 694405

DOI

10.3030/694405

Project closed

EC signature date 31 May 2016

Start date 1 September 2016

End date 30 November 2022

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 2 430 000,00

EU contribution

€ 2 430 000,00

Coordinated by

RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN
Germany

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Other (24)

From Harnack inequality to heat kernel estimates on metric measure spaces and applications

Author(s): Luca Tamanini
Published in: Arxiv Math, 2019
Publisher: AMS

THE STRONG BRUNN–MINKOWSKI INEQUALITY AND ITS EQUIVALENCE WITH THE CD CONDITION

Author(s): MATTIA MAGNABOSCO, LORENZO PORTINALE, TOMMASO ROSSI
Published in: Arxiv Math, 2022
Publisher: AMS

FIRST-ORDER HEAT CONTENT ASYMPTOTICS ON RCD(K,N) SPACES

Author(s): EMANUELE CAPUTO, TOMMASO ROSSI
Published in: Arxiv Math, 2022
Publisher: AMS

QUANTUM OPTIMAL TRANSPORT FOR AF-C-ALGEBRAS

Author(s): David Hornshaw
Published in: 2019
Publisher: Arxiv Math

Convex functions defined on metric spaces are pulled back to subharmonic ones by harmonic maps

Author(s): Hugo Lavenant, Léonard Monsaingeon, Luca Tamanini, Dmitry Vorotnikov
Published in: Arxiv Math, 2021
Publisher: AMS

L2-Wasserstein distances of tracial W*-algebras and their disintegration problem

Author(s): David Hornshaw
Published in: 2018
Publisher: Arxiv Math

Stable limit theorems on the Poisson space

Author(s): Ronan Herry
Published in: Arxiv Math, 2019
Publisher: AMS

Exponential Ergodicity for Time-Periodic McKean-Vlasov SDEs

Author(s): Panpan Ren, Karl-Theodor Sturm, Feng-Yu Wang,
Published in: Arxiv Math, 2021
Publisher: AMS

ON GLUING ALEXANDROV SPACES WITH LOWER RICCI CURVATURE BOUNDS

Author(s): VITALI KAPOVITCH, CHRISTIAN KETTERER, AND KARL-THEODOR STURM
Published in: Arxiv of Mathematics, 2020
Publisher: AMS
DOI: 10.48550/arxiv.2003.06242

THE RELATIVE HEAT CONTENT FOR SUBMANIFOLDS IN SUB-RIEMANNIAN GEOMETRY

Author(s): TOMMASO ROSSI
Published in: Arxiv Math, 2022
Publisher: AMS

THE BRUNN–MINKOWSKI INEQUALITY IMPLIES THE CD CONDITION IN WEIGHTED RIEMANNIAN MANIFOLDS

Author(s): MATTIA MAGNABOSCO, LORENZO PORTINALE, TOMMASO ROSSI
Published in: Arixv Math, 2022
Publisher: AMS

Convergence of metric measure spaces satisfying the CD condition for negative values of the dimension parameter

Author(s): Mattia Magnabosco, Chiara Rigoni, Gerardo Sosa
Published in: 2021
Publisher: Arxiv Math

A note about the strong maximum principle on RCD spaces

Author(s): Nicola Gigli, Chiara Rigoni
Published in: 2017
Publisher: Arxiv Math

Concentration of 1-Lipschitz functions on manifolds with boundary with Dirichlet boundary condition

Author(s): Yohei Sakurai
Published in: 2018
Publisher: Arxiv Math

Recognizing the flat torus among RCD∗(0,N) spaces via the study of the first cohomology group

Author(s): Nicola Gigli, Chiara Rigoni
Published in: 2017
Publisher: Arxiv Math

The isometry group of an ∗-space is Lie

Author(s): Gerardo Sosa
Published in: 2017
Publisher: Arxiv Math

One dimensional weighted Ricci curvature and displacement convexity of entropies

Author(s): Yohei Sakurai
Published in: 2018
Publisher: Arxiv Math

Ricci tensor on smooth metric measure space with boundary

Author(s): Bang-Xian Han
Published in: 2017
Publisher: Arxiv Math

Conformally invariant random fields, quantum Liouville measures, and random Paneitz operators on Riemannian manifolds of even dimension

Author(s): Schiavo, Lorenzo Dello; Herry, Ronan; Kopfer, Eva; Sturm, Karl-Theodor
Published in: Arxiv of Mathematics, Issue 1, 2021
Publisher: AMS
DOI: 10.48550/arxiv.2105.13925

Viscosity solutions of Hamilton-Jacobi equation in RCD(K,∞) spaces and applications to large deviations

Author(s): Nicola Gigli, Luca Tamanini, Dario Trevisan
Published in: Arxiv Math, 2022
Publisher: AMS

Partial derivatives in the nonsmooth setting

Author(s): Nicola Gigli, Chiara Rigoni
Published in: 2020
Publisher: Arxiv Math

ALMOST-RIEMANNIAN MANIFOLDS DO NOT SATISFY THE CURVATURE-DIMENSION CONDITION

Author(s): MATTIA MAGNABOSCO, TOMMASO ROSSI
Published in: Arxiv Math, 2022
Publisher: AMS

A Discovery Tour in Random Riemannian Geometry

Author(s): Lorenzo Dello Schiavo, Eva Kopfer, Karl-Theodor Sturm
Published in: Arxiv Math, 2020
Publisher: AMS

Heat kernel bounds and Ricci curvature for Lipschitz manifolds

Author(s): Mathias Braun, Chiara Rigoni
Published in: Arxiv Math, 2021
Publisher: AMS

Peer reviewed articles (22)

Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel

Author(s): Mathias Braun
Published in: Journal of Functional Analysis, 2022, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2022.109599

Functional inequalities for the heat flow on time-dependent metric measure spaces

Author(s): Eva Kopfer, Karl-Theodor Sturm
Published in: J. Lond. Math. Soc. (2), Issue 104, no. 2, 2021, Page(s) 926–955, ISSN 0024-6107
Publisher: Oxford University Press
DOI: 10.1112/jlms.12452

Transport inequalities for random point measures

Author(s): Nathael Gozlan; Ronan Herry; Giovanni Peccati
Published in: Journal of Functional Analysis, Issue 1, 2021, Page(s) Volume 281, Issue 9, 1 November 2021, 109 - 141, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2021.109141

Sobolev spaces on warped products

Author(s): Nicola Gigli, Bang-Xian Han
Published in: Journal of Functional Analysis, Issue 275/8, 2018, Page(s) 2059-2095, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2018.03.021

Order preservation and positive correlation for nonlinearFokker-Planck equation

Author(s): Panpan Ren
Published in: Electron. Commun. Probab., Issue 27, 2022, Page(s) 1–12., ISSN 1083-589X
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-ecp466

Singular McKean–Vlasov SDEs:Well-posedness, regularities andWang’s Harnack inequality

Author(s): Panpan Ren
Published in: Stochastic Processes and their Applications, Issue 156, 2023, Page(s) 291–311, ISSN 0304-4149
Publisher: Elsevier BV
DOI: 10.1016/j.spa.2022.11.010

Ricci Tensor on $$\mathrm{RCD}^*(K, N)$$ RCD ∗ (

Author(s): Bang-Xian Han
Published in: The Journal of Geometric Analysis, Issue 28/2, 2018, Page(s) 1295-1314, ISSN 1050-6926
Publisher: American Mathematical Society
DOI: 10.1007/s12220-017-9863-7

Second order differentiation formula on RCD$(K,N)$ spaces

Author(s): Nicola Gigli, Luca Tamanini
Published in: Rendiconti Lincei - Matematica e Applicazioni, Issue 29/2, 2018, Page(s) 377-386, ISSN 1120-6330
Publisher: Accademia Nazionale dei Lincei
DOI: 10.4171/RLM/811

Neumann heat flow and gradient flow for the entropy on non-convex domains

Author(s): Janna Lierl, Karl-Theodor Sturm
Published in: Calculus of Variations and Partial Differential Equations, Issue 57/1, 2018, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-017-1292-8

Heat Flow on Time-Dependent Metric Measure Spaces and Super-Ricci Flows

Author(s): Eva Kopfer, Karl-Theodor Sturm
Published in: Communications on Pure and Applied Mathematics, Issue 71/12, 2018, Page(s) 2500-2608, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/cpa.21766

Ricci tensor for diffusion operators and curvature-dimension inequalities under conformal transformations and time changes

Author(s): Karl-Theodor Sturm
Published in: Journal of Functional Analysis, Issue 275/4, 2018, Page(s) 793-829, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2018.03.022

Gradient flows for semiconvex functions on metric measure spaces – existence, uniqueness, and Lipschitz continuity

Author(s): Karl-Theodor Sturm
Published in: Proceedings of the American Mathematical Society, Issue 146/9, 2018, Page(s) 3985-3994, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/14061

Heat Flow with Dirichlet Boundary Conditions via Optimal Transport and Gluing of Metric Measure Spaces

Author(s): Angelo Profeta, Karl-Theodor Sturm
Published in: Calc. Var., Issue 59, 117 (2020), 2020, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-020-01774-w

Rigidity of cones with bounded Ricci curvature

Author(s): Matthias Erbar, Karl-Theodor Sturm
Published in: Journal European Mathematical Society, 2019, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House

Remarks about Synthetic Upper Ricci Bounds for Metric Measure Spaces

Author(s): Karl-Theodor Sturm
Published in: Tohoku Math. J. (2), Issue 73(4): 539-564 (2021), 2021, ISSN 0040-8735
Publisher: Tohoku University
DOI: 10.2748/tmj.20200717

Distribution-valued Ricci bounds for metric measure spaces, singular time changes, and gradient estimates for Neumann heat flows.

Author(s): Karl-Theodor Sturm
Published in: Geometric and Functional Analysis, Issue 30, 2020, Page(s) 1648–1711, ISSN 1420-8970
Publisher: Springer
DOI: 10.1007/s00039-020-00554-0

Tamed spaces -- Dirichlet spaces with distribution-valued Ricci bounds

Author(s): Erbar, Matthias; Rigoni, Chiara; Sturm, Karl-Theodor; Tamanini, Luca
Published in: Journal de Mathématiques Pures et Appliquées, Issue Volume 161, May 2022, Pages 1-69, 2020, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2022.02.002

Lie brackets of nonsmooth vector fields and commutation of their flows

Author(s): Chiara Rigoni; Eugene Stepanov; Dario Trevisan
Published in: Journal of the London Mathematical Society, Issue 1, 2022, Page(s) 1232-1256, ISSN 0024-6107
Publisher: Oxford University Press
DOI: 10.1112/jlms.12597

Optimal transport, gradient estimates, and pathwise brownian coupling on spaces with variable ricci bounds

Author(s): Braun, Mathias; Habermann, Karen; Sturm, Karl-Theodor
Published in: J. Math. Pures Appl., Issue 147 (9(, 2021, Page(s) 60–97., ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2021.01.002

Curvature-dimension conditions under time change

Author(s): Bang-Xian Han; Karl-Theodor Sturm
Published in: Annali di Matematica Pura ed Applicata (1923 -) volume 201, Issue 1, 2022, Page(s) pages 801–822, ISSN 0373-3114
Publisher: Nicola Zanichelli
DOI: 10.1007/s10231-021-01138-x

Heat flow regularity, Bismut's derivative formula, and pathwise Brownian couplings on Riemannian manifolds with Dynkin bounded Ricci curvature

Author(s): Mathias Braun, and Batu Güneysu
Published in: Electronic Journal of Probability, 2021, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/21-ejp703

Super-Ricci flows for metric measure spaces

Author(s): Karl-Theodor Sturm
Published in: J. Funct. Anal., Issue 275, no. 12,, 2018, Page(s) 3504–3569, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2018.07.014

Book chapters (1)

Random Riemannian geometry in 4 dimensions. Dirichlet forms and related topics,

Author(s): Karl-Theodor Sturm
Published in: Springer Proc. Math. Stat., Issue 394, 2022, Page(s) 493–510,, ISSN 2194-1009
Publisher: Springer