Structure Theorems for Modern Aspects of Geometric Measure Theory

Project Information

STMAGMT

Grant agreement ID: 948021

DOI

10.3030/948021

Project closed

EC signature date 11 September 2020

Start date 1 October 2020

End date 31 March 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 421 562,00

EU contribution

€ 1 421 562,00

Coordinated by

UNIVERSITY OF WARWICK
United Kingdom

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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

Peer reviewed articles (14)

Geometric characterizations of PI spaces: An overview of some modern techniques

Author(s): Emanuele Caputo
Published in: Indagationes Mathematicae, Issue 37, 2026, Page(s) 934-959, ISSN 0019-3577
Publisher: Elsevier BV
DOI: 10.1016/j.indag.2025.07.003

On the closability of differential operators

Author(s): Giovanni Alberti, David Bate, Andrea Marchese
Published in: Journal of Functional Analysis, Issue 289, 2025, Page(s) 111029, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2025.111029

Quantum optimal transport with convex regularization

Author(s): Emanuele Caputo, Augusto Gerolin, Nataliia Monina, Lorenzo Portinale
Published in: Journal of Functional Analysis, Issue 290, 2026, Page(s) 111262, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2025.111262

Bi-Lipschitz embeddings of the space of unordered $$m$$-tuples with a partial transportation metric

Author(s): David Bate, Ana Lucía Garcia Pulido
Published in: Mathematische Annalen, Issue 390, 2024, Page(s) 3109-3131, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-024-02831-x

Sobolev spaces via chains in metric measure spaces

Author(s): Emanuele Caputo, Nicola Cavallucci
Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2025, Page(s) 1-51, ISSN 0308-2105
Publisher: The RSE Scotland Foundation
DOI: 10.1017/prm.2025.10052

Poincaré inequality and energy of separating sets

Author(s): Emanuele Caputo, Nicola Cavallucci
Published in: Advances in Calculus of Variations, 2025, ISSN 1864-8258
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/acv-2024-0109

Generalized products and Lorentzian length spaces

Author(s): Elefterios Soultanis
Published in: Letters in Mathematical Physics, Issue 115, 2025, ISSN 1573-0530
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s11005-025-01910-7

A Geometric Approach to Poincaré Inequality and Minkowski Content of Separating Sets

Author(s): Emanuele Caputo, Nicola Cavallucci
Published in: International Mathematics Research Notices, Issue 2025, 2025, ISSN 1687-0247
Publisher: Oxford University Press (OUP)
DOI: 10.1093/imrn/rnae276

Weighted fractional Poincaré inequalities via isoperimetric inequalities

Author(s): Kim Myyryläinen, Carlos Pérez, Julian Weigt
Published in: Calculus of Variations and Partial Differential Equations, Issue 63, 2024, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-024-02813-6

Characterising 1-Rectifiable Metric Spaces via Connected Tangent Spaces

Author(s): David Bate, Phoebe Valentine
Published in: International Mathematics Research Notices, Issue 2026, 2026, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnag014

Typical Lipschitz images of rectifiable metric spaces

Author(s): David Bate, Jakub Takáč
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal), 2024, ISSN 0075-4102
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/crelle-2024-0004

Characterising rectifiable metric spaces using tangent spaces.

Author(s): David Bate
Published in: Inventiones Mathematicae, Issue 230, 2022, Page(s) 995–1070, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-022-01136-7

Closed BV-extension and W1,1-extension sets

Author(s): Emanuele Caputo, Jesse Koivu, Danka Lučić, Tapio Rajala
Published in: Journal of Functional Analysis, Issue 290, 2026, Page(s) 111319, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2025.111319

Ricci curvature bounded below and uniform rectifiability

Author(s): Matthew Hyde, Michele Villa, Ivan Yuri Violo
Published in: Annales Fennici Mathematici, Issue 49, 2024, ISSN 2737-114X
Publisher: Finnish Mathematical Society
DOI: 10.54330/afm.153338

Non-peer reviewed articles (1)

Qualitative Lipschitz to bi-Lipschitz decomposition

Author(s): David Bate
Published in: Analysis and Geometry in Metric Spaces, Issue 12, 2024, ISSN 2299-3274
Publisher: Walter de Gruyter GmbH
DOI: 10.1515/agms-2024-0005