ERC Starting Grant CURVATURE

PROJECT TIME-FRAME:  February 2019 - April 2025 

 PREVIOUS MEMBERS OF THE TEAM:

• Krzysztof Jan Ciosmak (PDRA) 

• Daniele Semola (PDRA)

• Alexis Michelat  (PDRA)

• Mustafa Alper Gunes (Research Associate)

• Dimitri Navarro (Ph. D. student)

• Clemens Sämann (PDRA) 

 ORGANIZED EVENTS:

• Optimal Transport and Geometric Analysis (Venice, 1-5 April 2019) 

• Metric measure spaces with symmetry and lower Ricci curvature bounds. BIRS: 22w5066. (7-12 August 2022)

PAPERS  (in inverse chronological order):

• K. J. Ciosmak, General localisation scheme I: theory, preprint arXiv:2312.12281, pp.1--69, (2023).

• K. J. Ciosmak, General localisation scheme II: applications, preprint arXiv:2312.13167 , pp.1--31, (2023)

•  F. Fiorani, A. Mondino, D. Semola, Monotonicity formula and stratification of the singular set of perimeter minimizers in RCD spaces, preprint arXiv:2307.06205, pp. 1--37, (2023).

• B. G. De Luca, N. De Ponti, A. Mondino, A. Tomasiello, Harmonic functions and gravity localization, Journal of High Energy Physics (JEHP) (accepted),  preprint arXiv:2306.05456, pp. 1--43, (2023). 

• N. Gigli, A. Mondino and D. Semola, On the notion of Laplacian bounds on RCD spaces and applications, Proceedings of the American Math. Society (accepted) preprint arXiv:2302.05474, pp. 1-12, (2023).

• B. G. De Luca, N. De Ponti, A. Mondino and A. Tomasiello, Gravity from thermodynamics: optimal transport and negative effective dimensions, Scipost Physics, 15, 039, (2023), pp.1--55  doi: 10.21468/SciPostPhys.15.2.039

• D. Barilari, A. Mondino, L. Rizzi, Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures, preprint arXiv:2211.07762, pp. 1--148, (2022).

• G. Antonelli, E. Pasqualetto, M. Pozzetta, D. Semola, Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds, Mathematische Annalen, https://doi.org/10.1007/s00208-023-02674-y ,42 pp.

• E. Brué, A. Mondino, D. Semola, The metric measure boundary of spaces with Ricci curvature bounded below, Geometric and Functional Analysis (GAFA), 33, pp.593–636 (2023), https://doi.org/10.1007/s00039-023-00626-x. 

• F. Cavalletti and A. Mondino, A review of Lorentzian synthetic theory of timelike Ricci curvature bounds,  General Relativity and Gravitation  54 (2022), no. 11, Paper No. 137, 39 pp.  Preprint Arxiv (2022).

• D. Navarro, Contractibility of moduli spaces of RCD(0,2) structures, preprint arXiv:2202.06659, 33 pp.

• G. Antonelli, E. Pasqualetto, M. Pozzetta, D. Semola, Sharp isoperimetric comparison on non-collapsed spaces with lower Ricci bounds,  preprint arXiv:2201.04916, 47 pp.  Annales scientifiques de l'École normale supérieure (in press).

• A. Mondino and D. Navarro,   Moduli spaces of compact RCD(0,N)-structures, Mathematische Annalen https://doi.org/10.1007/s00208-022-02493-7, preprint arXiv (2022).

• B. G. De Luca, N. De Ponti, A. Mondino and A. Tomasiello,  Cheeger bounds on spin-2 fields,  Journal of High Energy Physics (JHEP),  (2021), no. 12, Paper No. 217, 50 pp. Preprint arXiv (2021).

• M. A. Gunes and A. Mondino, A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(K,N) spaces, Proc. Amer. Math. Soc., Vol.  151 (2023), no. 1, 295–311.  Preprint arXiv (2021).

• E. Brué,  E. Pasqualetto and D. Semola, Constancy of the dimension in co-dimension one and locality of the unit normal on RCD(K,N) spaces, Annali Sc. Norm. Sup. Cl. Sci. (2022), Preprint arXiv (2021). 

• K. J. Ciosmak, Matrix Hölder's inequality and divergence formulation of optimal transport of vector measures, SIAM Journal on Mathematical Analysis, 53(6), 6932–6958, preprint arXiv (2021).

• K. J. Ciosmak, Optimal transport of vector measures, Calc. Var. PDE, Vol. 60, 230, (2021), preprint arXiv (2021)

• K. J. Ciosmak, Leaves decompositions in Euclidean spaces, Journal de Mathématiques Pures et Appliquées, Vol, 154, (2021), pp. 212-244, https://doi.org/10.1016/j.matpur.2021.08.003, preprint arXiv (2021)

• A. Mondino and D. Semola, Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from RCD(K,N) spaces to CAT(0) spaces, preprint  arXiv:2202.01590, pp. 1--48, (2022). American Journal of Mathematics  (in press).

• A. Mondino and D. Semola, Weak Laplacian bounds and minimal boundaries in non-smooth spaces with Ricci curvature lower bounds, Memoirs of the American Mathematical Society (accepted), Preprint arXiv (2021). 

• A. Michelat and A. Mondino,   Quantization of the Willmore Energy in Riemannian Manifolds, preprint  arXiv:2112.13831, pp. 1--82, (2021). 

• A. Mondino and A. Browne, Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity, J. Lond. Math. Soc. (2) 106 (2022), no. 3, 1844--1896. Preprint arXiv (2021).

• I. Mondello, A. Mondino and R. Perales,  An upper bound on the revised first Betti number and a torus stability result for RCD spaces,  Commentarii Mathematici Helvetici, Vol.  97 (2022), no. 3, 555--609, Preprint arXiv (2021).

• E. Brué,  Q. Deng and D. Semola, Improved regularity estimates for Lagrangian flows on RCD(K,N) spaces,  Nonlinear Analysis, Vol. 214, (2022), Paper No. 112609, 26 pp.  preprint arXiv (2021) 

• A. Mondino and C. Scharrer, A strict inequality for the minimisation of the Willmore functional under isoperimetric constraint, Advances in Calc. Var., https://doi.org/10.1515/acv-2021-0002,  Preprint arXiv (2020).

• E. Brué, A. Naber and D. Semola, Boundary regularity and stability for spaces with Ricci bounded below, Inventiones Math., Vol. 228, (2022), No. 2, 777-891,  Preprint arXiv (2020).

• N. De Ponti and A. Mondino, Entropy-Transport distances between unbalanced metric measure spaces, Probab. Theory Relat. Fields, Vol. 184, (2022), no. 1-2, 159–208 Preprint arXiv (2020)

• A. Mondino and M. Vedovato, A Talenti-type comparison theorem for RCD(K,N) spaces and applications, Calc. Var. and PDE, 60, 157 (2021), preprint arXIv (2020)

• N. De Ponti, A. Mondino and D. Semola, The equality case in Cheeger's and Buser's inequalities on RCD spaces, Journ. Funct. Analysis, Vol. 281 (3), (2021), 109022, preprint arXiv (2020)

• F. Cavalletti and A. Mondino, Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications, Cambridge Journal of  Mathematics (in press) preprint arXiv (2020)

• F. Cavalletti, A. Mondino and D. Semola, Quantitative Obata's Theorem, Analysis and PDE (accepted),  preprint arXiv (2019)

• V. Kapovitch and A. Mondino, On the topology and the boundary of N-dimensional RCD(K,N) spaces, Geometry & Topology 25 (2021) 445-495, DOI: 10.2140/gt.2021.25.445, preprint arXiv (2019)

• A. Mondino and C. Scharrer, Existence and Regularity of Spheres Minimising the Canham-Helfrich Energy, Arch. Rational Mech. Anal. 236, 1455–1485 (2020). https://doi.org/10.1007/s00205-020-01497-4  preprint arXiv (2019)

• N. De Ponti and A. Mondino, Sharp Cheeger-Buser type inequalities in RCD(K,∞)  spaces, J.  Geom.  Anal., Vol. 31, 2416–2438 (2021). https://doi.org/10.1007/s12220-020-00358-6,  preprint arXiv (2019)

• A. Mondino and S. Suhr, An optimal transport formulation of the Einstein equations of general relativity,  Journ. Europ. Math. Soc. (accepted), preprint arXiv (2018, revised 2021)

• A. Mondino and D. Semola, Polya-Szego inequality and Dirichlet p-spectral gap for non-smooth spaces with Ricci curvature bounded below, Journal de Mathématiques Pures et Appliquées,  Vol.137, (2020), pp 238-274, https://doi.org/10.1016/j.matpur.2019.10.005,  preprint arXiv (2018, revised 2019)

• F. Cavalletti and A. Mondino, New formulas for the Laplacian of distance functions and applications, Analysis and PDE, 13 (2020) 2091-2147, DOI: 10.2140/apde.2020.13.2091,  preprint arXiv (2018, revised 2019)