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

Información del proyecto

CURVATURE

Identificador del acuerdo de subvención: 802689

DOI

10.3030/802689

Proyecto cerrado

Fecha de la firma de la CE 27 Septiembre 2018

Fecha de inicio 1 Febrero 2019

Fecha de finalización 30 Abril 2025

Financiado con arreglo a

• EXCELLENT SCIENCE - European Research Council (ERC)

Coste total

€ 1 256 221,00

Aportación de la UE

€ 1 256 221,00

Coordinado por

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

CORDIS proporciona enlaces a los documentos públicos y las publicaciones de los proyectos de los programas marco HORIZONTE.

Los enlaces a los documentos y las publicaciones de los proyectos del Séptimo Programa Marco, así como los enlaces a algunos tipos de resultados específicos, como conjuntos de datos y «software», se obtienen dinámicamente de OpenAIRE .

Resultado final

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

Publicaciones

Peer reviewed articles (36)

Entropy-Transport distances between unbalanced metric measure spaces

Autores: Ponti, ND; Mondino, A
Publicado en: Probability Theory and Related Fields, Edición 01788051, 2022, ISSN 0178-8051
Editor: Springer Verlag
DOI: 10.1007/s00440-022-01159-4

Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds

Autores: Gioacchino Antonelli; Enrico Pasqualetto; Marco Pozzetta; Daniele Semola
Publicado en: Math. Annalen, 2023, ISSN 0025-5831
Editor: Springer Verlag
DOI: 10.1007/s00208-023-02674-y

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

Autores: Cavalletti, Fabio; Mondino, Andrea
Publicado en: Cambridge Journal of Mathematics, 2024, ISSN 2168-0930
Editor: 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

Autores: Bruè, Elia; Pasqualetto, Enrico; Semola, Daniele
Publicado en: Annali della Scuola normale superiore di Pisa - Classe di scienze, Edición 1, 2022, ISSN 0391-173X
Editor: Stampacchia Guido
DOI: 10.2422/2036-2145.202110_007

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

Autores: Vitali Kapovitch, Andrea Mondino
Publicado en: Geometry & Topology, Edición 25/1, 2021, Página(s) 445-495, ISSN 1465-3060
Editor: University of Warwick
DOI: 10.2140/gt.2021.25.445

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

Autores: Mustafa Gunes; Andrea Mondino
Publicado en: Proceedings of the American Mathematical Society, Edición 2, 2022, ISSN 0002-9939
Editor: American Mathematical Society
DOI: 10.1090/proc/16099

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

Autores: Gioacchino ANTONELLI, Enrico PASQUALETTO, Marco POZZETTA, Daniele SEMOLA
Publicado en: Annales Scientifiques de l'École Normale Supérieure, 2025, ISSN 0012-9593
Editor: Elsevier BV
DOI: 10.24033/asens.2601

Existence and Regularity of Spheres Minimising the Canham–Helfrich Energy

Autores: Andrea Mondino, Christian Scharrer
Publicado en: Archive for Rational Mechanics and Analysis, Edición 236/3, 2020, Página(s) 1455-1485, ISSN 0003-9527
Editor: Springer Verlag
DOI: 10.1007/s00205-020-01497-4

Leaves decompositions in Euclidean spaces

Autores: Krzysztof J. Ciosmak
Publicado en: Journal de Mathématiques Pures et Appliquées, 2021, ISSN 0021-7824
Editor: Elsevier BV
DOI: 10.1016/j.matpur.2021.08.003

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

Autores: Nicolò De Ponti, Andrea Mondino
Publicado en: The Journal of Geometric Analysis, Edición 31/3, 2021, Página(s) 2416-2438, ISSN 1050-6926
Editor: American Mathematical Society
DOI: 10.1007/s12220-020-00358-6

Gravity from thermodynamics: Optimal transport and negative effective dimensions

Autores: De Luca, B; De Ponti, N; Mondino, A; Tomasiello, A
Publicado en: SciPost Physics, 2023, ISSN 2542-4653
Editor: Scipost Foundation
DOI: 10.21468/scipostphys.15.2.039

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

Autores: Nicolò De Ponti, Andrea Mondino, Daniele Semola
Publicado en: Journal of Functional Analysis, Edición 281/3, 2021, Página(s) 109022, ISSN 0022-1236
Editor: Academic Press
DOI: 10.1016/j.jfa.2021.109022

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

Autores: Krzysztof Ciosmak
Publicado en: SIAM Journal on Mathematical Analysis, Edición 1, 2021, ISSN 0036-1410
Editor: 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

Autores: Mondello, I; Mondino, A; Perales, R
Publicado en: Commentarii Mathematici Helvetici, Edición 00102571, 2022, ISSN 0010-2571
Editor: Birkhauser Verlag
DOI: 10.4171/cmh/540

Fundamental groups and the Milnor conjecture

Autores: Elia Bruè, Aaron Naber, Daniele Semola
Publicado en: Annals of Mathematics, Edición 201, 2025, ISSN 0003-486X
Editor: Princeton University Press
DOI: 10.4007/annals.2025.201.1.4

Optimal transport of vector measures

Autores: Krzysztof Jan Ciosmak
Publicado en: Calculus of Variations and Partial Differential Equations, 2021, ISSN 0944-2669
Editor: Springer Verlag
DOI: 10.1007/s00526-021-02095-2

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

Autores: Andrea Mondino, Christian Scharrer
Publicado en: Advances in Calculus of Variations, Edición 0/0, 2021, ISSN 1864-8258
Editor: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/acv-2021-0002

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

Autores: Sämann, Clemens; Schinnerl, Benedict; Steinbauer, Roland; Švarc, Robert
Publicado en: Lett. Math. Phys., 2024, ISSN 0377-9017
Editor: Kluwer Academic Publishers
DOI: 10.1007/s11005-024-01804-0

Cheeger bounds on spin-two fields

Autores: Luca, GBD; Ponti, ND; Mondino, A; Tomasiello, A
Publicado en: Journal of High Energy Physics, 2021, ISSN 1029-8479
Editor: Institute of Physics Publishing
DOI: 10.1007/jhep12(2021)217

On the notion of Laplacian bounds on spaces and applications

Autores: Gigli, N; Mondino, A; Semola, D
Publicado en: Proceedings of the American Mathematical Society, 2023, ISSN 0002-9939
Editor: 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

Autores: Andrea Mondino, Daniele Semola
Publicado en: Journal de Mathématiques Pures et Appliquées, 2019, ISSN 0021-7824
Editor: Elsevier BV
DOI: 10.1016/j.matpur.2019.10.005

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

Autores: Andrea Mondino, Mattia Vedovato
Publicado en: Calculus of Variations and Partial Differential Equations, Edición 60/4, 2021, ISSN 0944-2669
Editor: Springer Verlag
DOI: 10.1007/s00526-021-01971-1

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

Autores: Mondino, A; Templeton-Browne, A
Publicado en: Journal of the London Mathematical Society, Edición 00246107, 2022, ISSN 0024-6107
Editor: Oxford University Press
DOI: 10.1112/jlms.12612

Harmonic functions and gravity localization

Autores: De Luca, B; De Ponti, N; Mondino, A; Tomasiello, A
Publicado en: Journal of High Energy Physics, 2023, ISSN 1029-8479
Editor: Institute of Physics Publishing
DOI: 10.1007/jhep09(2023)127

New formulas for the Laplacian of distance functions and applications

Autores: Fabio Cavalletti, Andrea Mondino
Publicado en: Analysis & PDE, Edición 13/7, 2020, Página(s) 2091-2147, ISSN 2157-5045
Editor: Mathematical Sciences Publishers
DOI: 10.2140/apde.2020.13.2091

Boundary regularity and stability for spaces with Ricci bounded below

Autores: Bru��, Elia; Naber, Aaron; Semola, Daniele
Publicado en: Inventiones Mathematicae, Edición 7, 2022, ISSN 0020-9910
Editor: Springer Verlag
DOI: 10.1007/s00222-021-01092-8

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

Autores: Elia Bruè; Qin Deng; Daniele Semola
Publicado en: Journal of Nonlinear Analysis Theory Methods and Applications, Edición 3, 2021, ISSN 0362-546X
Editor: Pergamon Press Ltd.
DOI: 10.1016/j.na.2021.112609

Quantitative Obata's Theorem

Autores: Cavalletti, Fabio; Mondino, Andrea; Semola, Daniele
Publicado en: Analysis and PDE, 2023, ISSN 2157-5045
Editor: Mathematical Sciences Publishers
DOI: 10.2140/apde.2023.16.1389

The metric measure boundary of spaces with Ricci curvature bounded below

Autores: Bruè, Elia; Mondino, Andrea; Semola, Daniele
Publicado en: Geometric and Functional Analysis, 2023, ISSN 1016-443X
Editor: Birkhauser Verlag
DOI: 10.1007/s00039-023-00626-x

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

Autores: Shouhei Honda, Andrea Mondino
Publicado en: Archiv der Mathematik, Edición 124, 2025, Página(s) 449-455, ISSN 0003-889X
Editor: Birkhauser Verlag
DOI: 10.1007/s00013-024-02091-w

An optimal transport formulation of the Einstein equations of general relativity

Autores: Andrea Mondino, Stefan Suhr
Publicado en: Journal of the European Math. Society, 2022, ISSN 1435-9855
Editor: European Mathematical Society Publishing House
DOI: 10.4171/jems/1188

A review of Lorentzian synthetic theory of timelike Ricci curvature bounds

Autores: Cavalletti, F; Mondino, A
Publicado en: General Relativity and Gravitation, 2022, ISSN 0001-7701
Editor: 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

Autores: Mondino, Andrea; Semola, Daniele
Publicado en: American Journal of Mathematics, 2024, ISSN 0002-9327
Editor: The Johns Hopkins University Press
DOI: 10.48550/arxiv.2202.01590

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

Autores: Barilari, Davide; Mondino, Andrea; Rizzi, Luca
Publicado en: Memoirs of the American Mathematical Society, 2024, ISSN 0065-9266
Editor: American Mathematical Society
DOI: 10.48550/arxiv.2211.07762

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

Autores: Andrea Mondino, Daniele Semola
Publicado en: Memoirs of the American Math. Soc., 2023, ISSN 0065-9266
Editor: American Mathematical Society

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

Autores: Mondino, A; Navarro, D
Publicado en: Math. Annalen, 2023, ISSN 0025-5831
Editor: Springer Verlag
DOI: 10.1007/s00208-022-02493-7