Published/Accepted papers

  1. Weak Laplacian bounds and minimal boundaries in non-smooth spaces with Ricci curvature lower bounds, (with A. Mondino), accepted by Mem. Amer. Math. Soc., (2023) [arXiv].​​
  2. The metric measure boundary of spaces with Ricci curvature bounded below, (with E. Bruè and A. Mondino), accepted by Geom. Funct. Anal., (2022), [arXiv].
  3. Constancy of the dimension in codimension one and locality of the unit normal on RCD(K,N) spaces, (with E. Bruè and E. Pasqualetto), accepted by Ann. Sc. Norm. Sup. Cl. Sci., (2022) [arXiv].
  4. Quantitative Obata's theorem​, (with F. Cavalletti and A. Mondino), accepted by Analysis & PDE, (2022), [arXiv]. 
  5. Rectifiability of the reduced boundary for sets of finite perimeter over RCD(K,N) spaces, (with E. Bruè and E. Pasqualetto), accepted by Journal of the European Mathematical Society, (2021), [arXiv].  ​
  6. Boundary regularity and stability for spaces with Ricci bounded below, (with E. Bruè and A. Naber), Invent. math. 228 (2022), no. 2, 777-891, [arXiv].
  7. Improved regularity estimates for Lagrangian flows on RCD(K,N) spaces, (with E. Bruè and Q. Deng) Nonlinear Analysis. 214 (2022), [arXiv].
  8. Rectifiability of RCD(K,N) spaces via δ splitting maps, (with E. Bruè and E. Pasqualetto) Ann. Fenn. Math. 46 (2021), no. 1, 465-482, [arXiv].
  9. The equality case in Cheeger's and Buser's inequalities on RCD spaces, (with N. De Ponti and A. Mondino) J. Funct. Anal. 281 (2021), no. 3, 36 pp., [arXiv].                                                                                            
  10. Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows, (with E. Bruè) Comm. Pure Appl. Math., 73 (2019), 1141-1204, [arXiv]. 
  11. Regularity of Lagrangian flows over RCD*(K, N) spaces,  ​(with E. Bruè) J. Reine Angew. Math. 765 (2020), 171-203, [arXiv].​  
  12. Polya-Szego inequality and Dirichlet p-spectral gap for non-smooth spaces with Ricci curvature bounded below,  (with A. Mondino).  J. Math. Pures Appl. (9), 137 (2020), 238-274, [arXiv].
  13. Volume Bounds for the Quantitative Singular Strata of Non Collapsed RCD Metric Measure Spaces, (with G. Antonelli and E. Bruè) Anal. Geom. Metr. Spaces 7 (2019), no. 1, 158-178, [arXiv].                                                                                                                                                                                      
  14. Rigidity of the 1-Bakry-Émery inequality and sets of finite perimeter in RCD spaces, (with L. Ambrosio and E. Bruè)  Geom. Funct. Anal. 29 (2019), no. 4, 949-1001, [arXiv].      ​                                                                                                                                       

Preprints


  1. Fundamental Groups and the Milnor Conjecture, (with E. Bruè and A. Naber), (2023), [arXiv].
  2. On the notion of Laplacian bounds on RCD spaces and applications, (with N. Gigli and A. Mondino), (2023), [arXiv]. 
  3. Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds, (with G. Antonelli, E. Pasqualetto and M. Pozzetta), (2022), [arXiv].​
  4. Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from RCD(K,N) to CAT(0) spaces, (with A. Mondino), (2022), [arXiv].
  5. ​Sharp isoperimetric comparison on non collapsed spaces with lower Ricci bounds, (with G. Antonelli, E. Pasqualetto and M. Pozzetta) (2022) [arXiv].​                                                                                                                                                                    

Books

  1. Lectures on Optimal Transport, (with L. Ambrosio and E. Bruè) La Matematica per il 3+2, (130), Springer (2021), 250 pp.                                                                                                                             

Academic works

PhD thesis, Recent developments about Geometric Analysis on RCD(K,N) spaces. Advisors: Prof. L. Ambrosio and Prof. A. Mondino.