Preprints

• A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds (with A. Mondino). Submitted,  arXiv:2401.03949.

• On the geometry of synthetic null hypersurfaces (with D. Manini and A. Mondino). Submitted, arXiv:2506.04934v1. 

Publications

1. The Monge problem in the Wiener space. Calc. Var and PDE, Vol. 45 (1-2) (2012), 101–124.

2. The Monge problem for distance cost in geodesic spaces (with S. Bianchini). Commun. Math. Phys., 318 (2013), 615–673.

3. Optimal transportation with branching distance costs and the obstacle problem. SIAM J. Math. Anal., Vol. 44 (2012), No. 1, 454–482.

4. Local Curvature-Dimension condition implies Measure-Contraction property (with K.-T. Sturm). J. Funct. Anal., 262 (2012), 5110–5127.

5. Existence and uniqueness of optimal transport maps (with M. Huesmann). Ann. I. H. Poincare ́ AN, 32 (2015) 1367–1377.

6. Self-Intersection of Optimal geodesics (with M. Huesmann). Bull. London Math. Soc., 46 (2014) 653–656.

7. A note on a residual subset of Lipschitz functions on metric spaces. Proceedings of Edinburgh Math. Society., Volume 58, Issue 3, 631–636.

8. Monge problem in metric spaces with Riemannian curvature-dimension condition. Nonlinear Analysis, 99 (2014), 136–151.

9. Decomposition of geodesics in the Wasserstein space and the globalization problem. Geom. Funct. Anal., Vol. 24 (2014) 493–551.

10. The polar cone of the set of monotone maps (with M. Westdickenberg). Proc. Amer. Math. Soc., 143 - 2 (2015), 781–787.

11. A simple proof of global existence for the 1D Pressureless Gas Dynamics Equations (with M. Sedjro and M. Westdickenberg). SIAM J. Math. Anal., 47 (2015), no. 1, 66–79.

12. Measure rigidity of Ricci curvature lower bounds (with A. Mondino). Advances Math., 286 (2016) 430–480.

13. Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds (with A. Mondino). Inventiones Math., 208 (2017) 803–849.

14. Tangent lines and Lipschitz differentiability spaces (with T. Rajala). Anal. Geom. Metr. Spaces, 4 (2016) 85–103.

15. Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds (with  A. Mondino). Geom. Topol., 21 (2017) 603–645.

16. Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds (with A. Mondino). Rendiconti Lincei Matematica e Applicazioni, Volume 29, 3 (2018) 413–430.

17. Optimal maps in essentially non-branching spaces (with A. Mondino). Commun. Contemp. Math., 06 (2017) 19.

18. An overview of L1 optimal transportation on metric measure spaces. Measure Theory in Non-Smooth Spaces, book chapter, edited by N. Gigli, De Gruyter Open.

19. Rigidity for critical points in the Levy-Gromov inequality (with F. Maggi and A. Mondino). Math. Z., (2018) 289: 1191.

20. Almost euclidean Isoperimetric Inequalities in spaces satisfying local Ricci curvature lower bounds (with A. Mondino). Int. Math. Res. Not., 2020 (2020), 1481–1510.

21. A variational time discretization for the compressible Euler equations (with M. Sedjro and M. Westdickenberg). Trans. Amer. Math. Soc., 371 (2019), 5083-5155. 

22. Quantitative isoperimetry à la Levy-Gromov (with F. Maggi and A. Mondino). Comm. Pure Appl. Math., LXXII (2019), 1631–1677.

23. Isoperimetric inequality under Measure-Contraction property (with F. Santarcangelo). J. Funct. Anal., 277 (2019),  2893-2917.

24. New formulas for the Laplacian of distance functions and applications (with A. Mondino). Analysis & PDE, arXiv:1803.09687.

25. Displacement convexity of Entropy and the distance cost Optimal Transportation (with N. Gigli and F. Santarcangelo). Annales de la faculté des sciences de Toulouse,  arXiv:2005.00243.

26. Independence of synthetic Curvature Dimension conditions on transport distance exponent (with A. Akdemir, A. Colinet, R. J. McCann and F. Santarcangelo). Trans. Amer. Math. Soc., arXiv:2007.10980.

27. The Globalization Theorem for the Curvature Dimension Condition (with E. Milman). Inventiones Math.,  arXiv:1612.07623.

28. Quantitative Obata’s Theorem (with A. Mondino and D. Semola). Analysis & PDE, Vol. 16 (2023), No. 6, pp. 1389-1431,  arXiv:1910.06637.

29. Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications (with A. Mondino). Camb. J. Math., Vol 12 (2024), No. 2, pp 417-534. 

30. Indeterminacy estimates and the size of nodal sets in singular spaces (with S. Farinelli). Advances Math., arXiv:2011.04409.

31. Isoperimetric inequality in noncompact MCP spaces (with D. Manini). Proc. Amer. Math. Soc., 150 (2022), 3537–3548, DOI: https://doi.org/10.1090/proc/15945.

32. A review of Lorentzian synthetic theory of timelike Ricci curvature bounds (with A. Mondino). General Relativity and Gravitation, volume 54, Article number: 137 (2022).

33. Geometry of Grassmannians and optimal transport of quantum states (with P. Antonini). Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), arXiv:2104.02616.

34. A proof of the Hamiltonian Thom Isotopy Lemma (with P. Antonini and A. Lerario). Note di Matematica, Vol 43 (2023), issue 2. 

35. Rigidities of Isoperimetric inequality under nonnegative Ricci curvature (with D. Manini). J. Eur. Math. Soc.., arXiv:2207.03423.

36. Optimal transport between algebraic hypersurfaces (with P. Antonini and A. Lerario). Geom. Funct. Anal., arXiv:2212.10274.

37. Optimal transport on null hypersurfaces and the null energy condition (with D. Manini and A. Mondino). Commun. Math. Phys., DOI 10.1007/s00220-025-05345-y, arXiv:2408.08986.

Edita

1. Special Issue on Metric measure spaces, Ricci curvature, and optimal transport (with M. Erbar, J. Maas and K.-Th. Sturm). Indag. Math. (N.S.) 37 (2026), no. 3.

Proceedings 

1. The globalization theorem for the curvature-dimension condition (with E. Milman). Proceedings of the International Congress of Basic Science (2024). 

2. The Monge problem in geodesic spaces (with S. Bianchini). The IMA Volumes in Mathematics and its Applications, Vol. 153, 217–234.