Metric measure spaces and Ricci curvature — analytic, geometric, and probabilistic challenges | RicciBounds | Project | Results | H2020 | CORDIS

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

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

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

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

Publications

Share this page

Download