Optimal transport techniques in the geometric analysis of spaces with curvature bounds

Project Information

CURVATURE

Grant agreement ID: 802689

DOI

10.3030/802689

Project closed

EC signature date 27 September 2018

Start date 1 February 2019

End date 30 April 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 256 221,00

EU contribution

€ 1 256 221,00

Coordinated by

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom

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 .

Deliverables

Open Research Data Pilot (1)

Data Management Plan

The green open access platform ORA of Oxford makes available the papers accepted for publication in the final non published formMoreover all the papers of the PI will be posted to the green open access platform arXiv

Publications

Peer reviewed articles (36)

Entropy-Transport distances between unbalanced metric measure spaces

Author(s): Ponti, ND; Mondino, A
Published in: Probability Theory and Related Fields, Issue 01788051, 2022, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-022-01159-4

Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds

Author(s): Gioacchino Antonelli; Enrico Pasqualetto; Marco Pozzetta; Daniele Semola
Published in: Math. Annalen, 2023, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-023-02674-y

Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications

Author(s): Cavalletti, Fabio; Mondino, Andrea
Published in: Cambridge Journal of Mathematics, 2024, ISSN 2168-0930
Publisher: International Press
DOI: 10.48550/arxiv.2004.08934

Constancy of the dimension in codimension one and locality of the unit normal on $\mathrm{RCD}(K,N)$ spaces

Author(s): Bruè, Elia; Pasqualetto, Enrico; Semola, Daniele
Published in: Annali della Scuola normale superiore di Pisa - Classe di scienze, Issue 1, 2022, ISSN 0391-173X
Publisher: Stampacchia Guido
DOI: 10.2422/2036-2145.202110_007

On the topology and the boundary ofN–dimensional RCD(K,N) spaces

Author(s): Vitali Kapovitch, Andrea Mondino
Published in: Geometry & Topology, Issue 25/1, 2021, Page(s) 445-495, ISSN 1465-3060
Publisher: University of Warwick
DOI: 10.2140/gt.2021.25.445

A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(,) spaces

Author(s): Mustafa Gunes; Andrea Mondino
Published in: Proceedings of the American Mathematical Society, Issue 2, 2022, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/16099

Sharp isoperimetric comparison on non-collapsed spaces with lower Ricci bounds

Author(s): Gioacchino ANTONELLI, Enrico PASQUALETTO, Marco POZZETTA, Daniele SEMOLA
Published in: Annales Scientifiques de l'École Normale Supérieure, 2025, ISSN 0012-9593
Publisher: Elsevier BV
DOI: 10.24033/asens.2601

Existence and Regularity of Spheres Minimising the Canham–Helfrich Energy

Author(s): Andrea Mondino, Christian Scharrer
Published in: Archive for Rational Mechanics and Analysis, Issue 236/3, 2020, Page(s) 1455-1485, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-020-01497-4

Leaves decompositions in Euclidean spaces

Author(s): Krzysztof J. Ciosmak
Published in: Journal de Mathématiques Pures et Appliquées, 2021, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2021.08.003

Sharp Cheeger–Buser Type Inequalities in $$ \mathsf {RCD}(K,\infty )$$ Spaces

Author(s): Nicolò De Ponti, Andrea Mondino
Published in: The Journal of Geometric Analysis, Issue 31/3, 2021, Page(s) 2416-2438, ISSN 1050-6926
Publisher: American Mathematical Society
DOI: 10.1007/s12220-020-00358-6

Gravity from thermodynamics: Optimal transport and negative effective dimensions

Author(s): De Luca, B; De Ponti, N; Mondino, A; Tomasiello, A
Published in: SciPost Physics, 2023, ISSN 2542-4653
Publisher: Scipost Foundation
DOI: 10.21468/scipostphys.15.2.039

The equality case in Cheeger's and Buser's inequalities on RCD spaces

Author(s): Nicolò De Ponti, Andrea Mondino, Daniele Semola
Published in: Journal of Functional Analysis, Issue 281/3, 2021, Page(s) 109022, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2021.109022

Matrix Hölder's Inequality and Divergence Formulation of Optimal Transport of Vector Measures

Author(s): Krzysztof Ciosmak
Published in: SIAM Journal on Mathematical Analysis, Issue 1, 2021, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1367520

An upper bound on the revised first Betti number and a torus stability result for RCD spaces

Author(s): Mondello, I; Mondino, A; Perales, R
Published in: Commentarii Mathematici Helvetici, Issue 00102571, 2022, ISSN 0010-2571
Publisher: Birkhauser Verlag
DOI: 10.4171/cmh/540

Fundamental groups and the Milnor conjecture

Author(s): Elia Bruè, Aaron Naber, Daniele Semola
Published in: Annals of Mathematics, Issue 201, 2025, ISSN 0003-486X
Publisher: Princeton University Press
DOI: 10.4007/annals.2025.201.1.4

Optimal transport of vector measures

Author(s): Krzysztof Jan Ciosmak
Published in: Calculus of Variations and Partial Differential Equations, 2021, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-021-02095-2

A strict inequality for the minimization of the Willmore functional under isoperimetric constraint

Author(s): Andrea Mondino, Christian Scharrer
Published in: Advances in Calculus of Variations, Issue 0/0, 2021, ISSN 1864-8258
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/acv-2021-0002

Cut-and-paste for impulsive gravitational waves with $\Lambda$: The mathematical analysis

Author(s): Sämann, Clemens; Schinnerl, Benedict; Steinbauer, Roland; Švarc, Robert
Published in: Lett. Math. Phys., 2024, ISSN 0377-9017
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11005-024-01804-0

Cheeger bounds on spin-two fields

Author(s): Luca, GBD; Ponti, ND; Mondino, A; Tomasiello, A
Published in: Journal of High Energy Physics, 2021, ISSN 1029-8479
Publisher: Institute of Physics Publishing
DOI: 10.1007/jhep12(2021)217

On the notion of Laplacian bounds on spaces and applications

Author(s): Gigli, N; Mondino, A; Semola, D
Published in: Proceedings of the American Mathematical Society, 2023, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/16550

Polya-Szego inequality and Dirichlet p-spectral gap for non-smooth spaces with Ricci curvature bounded below

Author(s): Andrea Mondino, Daniele Semola
Published in: Journal de Mathématiques Pures et Appliquées, 2019, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2019.10.005

A Talenti-type comparison theorem for $${{\,\mathrm{RCD}\,}}(K,N)$$ spaces and applications

Author(s): Andrea Mondino, Mattia Vedovato
Published in: Calculus of Variations and Partial Differential Equations, Issue 60/4, 2021, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-021-01971-1

Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity

Author(s): Mondino, A; Templeton-Browne, A
Published in: Journal of the London Mathematical Society, Issue 00246107, 2022, ISSN 0024-6107
Publisher: Oxford University Press
DOI: 10.1112/jlms.12612

Harmonic functions and gravity localization

Author(s): De Luca, B; De Ponti, N; Mondino, A; Tomasiello, A
Published in: Journal of High Energy Physics, 2023, ISSN 1029-8479
Publisher: Institute of Physics Publishing
DOI: 10.1007/jhep09(2023)127

New formulas for the Laplacian of distance functions and applications

Author(s): Fabio Cavalletti, Andrea Mondino
Published in: Analysis & PDE, Issue 13/7, 2020, Page(s) 2091-2147, ISSN 2157-5045
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/apde.2020.13.2091

Boundary regularity and stability for spaces with Ricci bounded below

Author(s): Bru��, Elia; Naber, Aaron; Semola, Daniele
Published in: Inventiones Mathematicae, Issue 7, 2022, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-021-01092-8

Improved regularity estimates for Lagrangian flows on RCD(K,N) spaces

Author(s): Elia Bruè; Qin Deng; Daniele Semola
Published in: Journal of Nonlinear Analysis Theory Methods and Applications, Issue 3, 2021, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.na.2021.112609

Quantitative Obata's Theorem

Author(s): Cavalletti, Fabio; Mondino, Andrea; Semola, Daniele
Published in: Analysis and PDE, 2023, ISSN 2157-5045
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/apde.2023.16.1389

The metric measure boundary of spaces with Ricci curvature bounded below

Author(s): Bruè, Elia; Mondino, Andrea; Semola, Daniele
Published in: Geometric and Functional Analysis, 2023, ISSN 1016-443X
Publisher: Birkhauser Verlag
DOI: 10.1007/s00039-023-00626-x

Poincaré inequality for one-forms on four manifolds with bounded Ricci curvature

Author(s): Shouhei Honda, Andrea Mondino
Published in: Archiv der Mathematik, Issue 124, 2025, Page(s) 449-455, ISSN 0003-889X
Publisher: Birkhauser Verlag
DOI: 10.1007/s00013-024-02091-w

An optimal transport formulation of the Einstein equations of general relativity

Author(s): Andrea Mondino, Stefan Suhr
Published in: Journal of the European Math. Society, 2022, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1188

A review of Lorentzian synthetic theory of timelike Ricci curvature bounds

Author(s): Cavalletti, F; Mondino, A
Published in: General Relativity and Gravitation, 2022, ISSN 0001-7701
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10714-022-03004-4

Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from $\mathrm{RCD}(K,N)$ spaces to $\mathrm{CAT}(0)$ spaces

Author(s): Mondino, Andrea; Semola, Daniele
Published in: American Journal of Mathematics, 2024, ISSN 0002-9327
Publisher: The Johns Hopkins University Press
DOI: 10.48550/arxiv.2202.01590

Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures

Author(s): Barilari, Davide; Mondino, Andrea; Rizzi, Luca
Published in: Memoirs of the American Mathematical Society, 2024, ISSN 0065-9266
Publisher: American Mathematical Society
DOI: 10.48550/arxiv.2211.07762

Weak Laplacian bounds and minimal boundaries in non-smooth spaces with Ricci curvature lower bounds

Author(s): Andrea Mondino, Daniele Semola
Published in: Memoirs of the American Math. Soc., 2023, ISSN 0065-9266
Publisher: American Mathematical Society

Moduli spaces of compact RCD(0,N)-structures

Author(s): Mondino, A; Navarro, D
Published in: Math. Annalen, 2023, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-022-02493-7