Papers
11) D. Bate, E. Caputo, J. Takáč, P. Valentine, P. Wald, Structure of metric 1-currents: approximation by normal currents and representation results. Preprint (2025), 41 pp, arXiv.
10) E. Caputo, D. Lučić, J. Koivu, T. Rajala, Closed BV-extension and W^{1,1}-extension sets. Preprint (2025), 42 pp, arXiv.
9) E. Caputo, Geometric characterizations of PI spaces: an overview of some modern techniques. Indagationes Mathematicae, 2025, ISSN 0019-3577, https://doi.org/10.1016/j.indag.2025.07.003 (2025), arXiv (28 pp).
8) E. Caputo, A. Gerolin, N. Monina, L. Portinale, Quantum optimal transport with convex regularization. Preprint (2024), 39 pp, arXiv (submitted).
7) E. Caputo, N. Cavallucci, Sobolev spaces via chains in metric measure spaces. Proc. of the Royal Society of Edinburgh: Section A Mathematics. Published online 2025:1-51. doi:10.1017/prm.2025.10052, arXiv (52pp).
6) E. Caputo, N. Cavallucci, A geometric approach to Poincaré inequality and Minkowski content of separating sets. International Mathematics Research Notices, Volume 2025, Issue 1, January 2025, rnae276 (2025), arXiv (30 pp).
5) E. Caputo, N. Cavallucci, Poincaré inequality and energy of separating sets. Advances in Calculus of Variations, 2025. DOI:10.1515/acv-2024-0109. (2025), arXiv (37 pp).
4) E. Caputo, M, Lučić, E. Pasqualetto, I. Vojnović, On the integration of Banach modules and its applications to vector calculus on RCD spaces. Revista Matemática Complutense, 1-34 (2024), arXiv (22 pp).
3) E. Caputo, J. Koivu, T. Rajala, Sobolev, BV and perimeter extension in metric measure spaces. Ann. Fenn. Math. Issue Vol.49, No. 1, 130-165 (2024), arXiv (31 pp).
2) E. Caputo, T. Rossi, First order heat content asymptotics on RCD(K,N) spaces. Nonlinear Analysis, 238, Article 113385, (2024). arXiv (46pp).
1) E. Caputo, N. Gigli and E. Pasqualetto, Parallel transport on non-collapsed RCD(K,N) spaces. Journal für die Reine und Angewandte Mathematik (Crelle's Journal) , vol. 2025, no. 819, 2025, pp. 135-204 (2024), 56 pp. arXiv .
In preparation
12) E. Caputo, F. Nobili, T. Rossi, Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization.
13) E. Caputo, N. Cavallucci, Disconnection dimension and Poincaré inequality in spaces with curvature bounded above.
PhD thesis: Existence and uniqueness of parallel transport on non-collapsed RCD(K,N) spaces. Available at the following link.
Lecture notes
Functions of bounded variation, 144p (with M. Caponi, course by G. Dal Maso)
List of coauthors (in alphabetic order)
David Bate (Warwick)
Nicola Cavallucci (EPF Lausanne)
Augusto Gerolin (uOttawa)
Nicola Gigli (SISSA, Trieste)
Jesse Koivu (Jyväskylä)
Danka Lučić (Jyväskylä)
Milica Lučić (Novi Sad)
Nataliia Monina (uOttawa)
Francesco Nobili (Pisa)
Enrico Pasqualetto (Jyväskylä)
Lorenzo Portinale (Bonn)
Tapio Rajala (Jyväskylä)
Tommaso Rossi (Sorbonne)
Jakub Takáč (Warwick)
Phoebe Valentine (Warwick)
Ivana Vojnović (Novi Sad)
Pietro Wald (Warwick)