L. Ambrosio, N. Gigli, G. Savaré: Gradient flows with metric and differentiable structures, and applications to the Wasserstein space (Accepted Paper) 2003 N. Gigli: On the geometry of the space of probability measures endowed with the quadratic optimal transport distance (Ph.D. Thesis) 2008 L. Ambrosio, N. Gigli: Construction of the parallel transport in the Wasserstein space Methods and Applications of Analysis (Accepted Paper) 2008 N. Gigli: On Hölder continuity in time of the optimal transport map towards measures along a curve Proceedings of the Edinburgh Mathematical Society (Accepted Paper) 2008 N. Gigli: On the weak closure of convex sets of Probability measures Rendiconti di matematica (Accepted Paper) 2009 N. Gigli: On the inverse implication of Brenier-McCann theorems and the structure of $(P_2(M),W_2)$ Meth. Appl. of Anal. (Accepted Paper) 2009 N. Gigli: Second order analysis on (P_2(M),W_2) Memoirs of the American Mathematical Society (Accepted Paper) 2009 N. Gigli, F. Otto: Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric (Accepted at Calc.Var and PDE) 2010 N. Gigli, K. Kuwada, S. I. Ohta: Heat Flow on Alexandrov spaces (Accepted at CPAM) 2010 N. Gigli, S. I. Ohta: First variation formula in Wasserstein spaces over compact Alexandrov spaces Canad. Math. Bull. (Accepted Paper) 2010 N. Gigli: On the Heat flow on metric measure spaces: existence, uniqueness and stability Calc. Var. Part. Diff. Eq. (Accepted Paper) 2010 A. Figalli, N. Gigli: A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions J. Math. Pures Appl. 2010 N. Gigli, S. J. N. Mosconi: A variational approach to the Navier-Stokes equations (Accepted at Bullettin des Sciences Mathematiques) 2011 L. Ambrosio, N. Gigli: A user's guide to optimal transport () 2011 N. Gigli: Optimal maps in non branching spaces with Ricci curvature bounded from below (Accepted at GAFA) 2011 L. Ambrosio, N. Gigli, G. Savaré: Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below (Submitted Paper) 2011 N. Gigli: Geometric and analytic properties of some non smooth structures (Memoire HDR) 2011 L. Ambrosio, N. Gigli, G. Savaré: Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces (Submitted Paper) 2011 N. Gigli, M. Ledoux: From log Sobolev to Talagrand: a quick proof (Accepted Paper: DCDS-A) 2011 L. Ambrosio, N. Gigli, G. Savaré: Metric measure spaces with Riemannian Ricci curvature bounded from below (Submitted Paper) 2011 A. Figalli, N. Gigli: Local semiconvexity of Kantorovich potentials on non-compact manifolds ESAIM Control Optim. Calc. Var. 2011 N. Gigli: On the relation between the curvature-dimension condition and the Bochner inequality (Preprint) 2012 L. Ambrosio, N. Gigli, G. Savaré: Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case (Preprint) 2012 N. Gigli, J. Maas: Gromov-Hausdorff convergence of discrete transportation metrics (Submitted Paper) 2012 N. Gigli, S. J. N. Mosconi: The Abresch-Gromoll inequality in a non-smooth setting (Submitted Paper) 2012 L. Ambrosio, N. Gigli, A. Mondino, T. Rajala: Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure Transactions of the AMS (Accepted Paper) 2012 N. Gigli: On the differential structure of metric measure spaces and applications (Preprint) 2012 L. Ambrosio, N. Gigli, G. Savaré: Bakry-Emery curvature-dimension condition and Riemannian Ricci curvature bounds (Submitted Paper) 2012 N. Gigli, A. Mondino: A PDE approach to nonlinear potential theory in metric measure spaces Journal de Math. Pures et Appl. 2012 N. Gigli: The splitting theorem in non-smooth context (Submitted Paper) 2013 N. Gigli, T. Rajala, K. T. Sturm: Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below (Submitted Paper) 2013 N. Gigli: An overview on the proof of the splitting theorem in non-smooth context (Submitted Paper) 2013 N. Gigli, A. Mondino, T. Rajala: Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below J. Reine Angew. Math. (Accepted Paper) 2013 N. Gigli, A. Mondino, G. Savaré: Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows Proceedings of the London Mathematical Society (Accepted Paper) 2013 N. Gigli, A. Mondino, T. Rajala: Euclidean spaces as weak tangents of infinitesimally Hilbertian metric spaces with Ricci curvature bounded below (preprint) http://arxiv.org/abs/1304.5359 2013 N. Gigli, S. J. N. Mosconi: The abstract Lewy Stampacchia inequality and applications (Preprint) 2014 N. Gigli, C. Mantegazza: A Flow Tangent to the Ricci Flow via Heat Kernels and Mass Transport Advances in Math. Vol. 250, p. 74-104, 2014 N. Gigli: Nonsmooth differential geometry - An approach tailored for spaces with Ricci curvature bounded from below (Preprint) 2014 N. Gigli, B. Han: The continuity equation on metric measure spaces Calculus of Variations and Partial Differential Equations Vol. 53, p. 149-177, 2015 G. De Philippis, N. Gigli: From volume cone to metric cone in the nonsmooth setting Geom. Funct. Anal. (Accepted Paper) http://arxiv.org/abs/1512.03113 2015 N. Gigli, E. Pasqualetto: Behaviour of the reference measure on $\sf RCD$ spaces under charts (Preprint) p. 17, 2016 N. Gigli, B. Han: Independence on p of weak upper gradients on RCD spaces Journal of Functional Analysis Vol. 271, p. 1-11, 2016 L. Ambrosio, S. Di Marino, N. Gigli: Perimeter as relaxed Minkowski content in metric measure spaces Nonlinear Analysis: Theory, Methods & Applications (Submitted Paper) http://arxiv.org/abs/1603.08412 Vol. 153, p. 78-88, 2016 N. Gigli, E. Pasqualetto: Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces (Submitted Paper) 2016 N. Gigli, L. Tamanini: Second order differentiation formula on compact $RCD^*(K,N)$ spaces (Submitted Paper) 2017 N. Gigli: Lecture notes on differential calculus on RCD spaces (Preprint) 2017 N. Gigli, C. Rigoni: Recognizing the flat torus among $RCD^*(0,N)$ spaces via the study of the first cohomology group (Submitted Paper) 2017 N. Gigli, C. Rigoni: A note about the strong maximum principle on $RCD$ spaces (Preprint) 2017 G. De Philippis, N. Gigli: Non-collapsed spaces with Ricci curvature bounded from below (Preprint) http://arxiv.org/abs/1708.02060 2017 N. Gigli, C. Ketterer, K. Kuwada, S. I. Ohta: Rigidity for the spectral gap on $RCD(K,\infty)$-spaces (preprint) http://arxiv.org/abs/1709.04017 2017 N. Gigli, E. Pasqualetto: Differential structure associated to axiomatic Sobolev spaces (Preprint) p. 14, 2018 N. Gigli, E. Pasqualetto, E. Soultanis: Differential of metric valued Sobolev maps (Submitted Paper) 2018 S. Di Marino, N. Gigli, E. Pasqualetto, E. Soultanis: Infinitesimal Hilbertianity of locally ${\rm Cat}(\kappa)$-spaces (Submitted Paper) http://arxiv.org/abs/1812.02086 2018 N. Gigli, E. Pasqualetto: On the notion of parallel transport on $\sf RCD$ spaces (preprint) http://arxiv.org/abs/1803.05374 2018 N. Gigli, L. Tamanini: Second order differentiation formula on $RCD(K,N)$ spaces Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. (Proceedings) 2018 N. Gigli, B. Han: Sobolev Spaces on Warped Products Journal of Functional Analysis 2018 N. Gigli: Riemann curvature tensor on ${\sf RCD}$ spaces and possible applications (preprint) http://arxiv.org/abs/1902.02282 2019 C. Debin, N. Gigli, E. Pasqualetto: Quasi-continuous vector fields on RCD spaces (preprint) http://arxiv.org/abs/1903.04302 2019 N. Gigli, A. Tyulenev: Korevaar-Schoen's directional energy and Ambrosio's regular Lagrangian flows (Preprint) 2019 N. Gigli, A. Tyulenev: Korevaar-Schoen's energy on strongly rectifiable spaces (Preprint) http://arxiv.org/abs/2002.07440 2020 S. Di Marino, N. Gigli, A. Pratelli: Global Lipschitz extension preserving local constants Rend. Lincei Mat. Appl. 2020 N. Gigli, C. Rigoni: Partial derivatives in the nonsmooth setting (Submitted Paper) 2020 F. Cavalletti, N. Gigli, F. Santarcangelo: Displacement convexity of Entropy and the distance cost Optimal Transportation Annales de la faculté des sciences de Toulouse (Accepted Paper) 2020 N. Gigli, L. Tamanini: Benamou-Brenier and duality formulas for the entropic cost on $RCD^*(K,N)$ spaces Probab. Theory Related Fields 2020 N. Gigli, F. Nobili: A differential perspective on Gradient Flows on ${\sf CAT}()$-spaces and applications J. Geom. Anal. 2021 N. Gigli, I. Y. Violo: Monotonicity formulas for harmonic functions in ${\rm RCD}(0,N)$ spaces The Journal of Geometric Analysis 2021 N. Gigli, L. Tamanini: Second order differentiation formula on $RCD^*(K,N)$ spaces J. Eur. Math. Soc. (JEMS) 2021 C. Brena, N. Gigli, S. Honda, X. Zhu: Weakly non-collapsed RCD spaces are strongly non-collapsed J. Reine Angew. Math. (Crelle's Journal) 2021 E. Caputo, N. Gigli, E. Pasqualetto: Parallel transport on non-collapsed $\mathsf{RCD}(K,N)$ spaces Journal für die reine und angewandte Mathematik 2021 N. Gigli, D. Lui, E. Pasqualetto: Duals and pullbacks of normed modules (preprint) http://arxiv.org/abs/2207.04972 2022 N. Gigli, F. Nobili: A first-order condition for the independence on $p$ of weak gradients J. Funct. Anal. 2022 L. Gennaioli, N. Gigli: A note about charts built by Eriksson-Bique and Soultanis on metric measure spaces Canadian Mathematical Bulletin 2022 N. Gigli: On the regularity of harmonic maps from ${\sf RCD}(K,N)$ to ${\sf CAT}(0)$ spaces and related results (preprint) http://arxiv.org/abs/2204.04317 2022 C. Brena, N. Gigli: Local vector measures Journal of Functional Analysis 2022 C. Brena, N. Gigli: Calculus and fine properties of functions of bounded variation on RCD spaces The Journal of Geometric Analysis 2022 C. Brena, N. Gigli: Fine representation of Hessian of convex functions and Ricci tensor on RCD spaces Potential Anal. 2023 C. Brena, N. Gigli: About the general chain rule for functions of bounded variation Nonlinear Analysis 2023 N. Gigli, F. Marconi: A general splitting principle on RCD spaces and applications to spaces with positive spectrum (preprint) http://arxiv.org/abs/2312.06252 2023 N. Gigli: De Giorgi and Gromov working together (preprint) http://arxiv.org/abs/2306.14604 2023 N. Gigli, A. Mondino, D. Semola: On the notion of Laplacian bounds on $\mathrm{RCD}$ spaces and applications Proc. Amer. Math. Soc. Vol. 152, p. 829--841, 2024 N. Gigli, S. Vincini: Stability of the heat flow under convergence in concentration and consequences (preprint) http://arxiv.org/abs/2410.05011 2024 N. Gigli, L. Tamanini, D. Trevisan: Viscosity solutions of Hamilton-Jacobi equation in $RCD(K,\infty)$ spaces and applications to large deviations Potential Analysis 2024 M. Braun, N. Gigli, R. J. McCann, A. Ohanyan, C. Sämann: An elliptic proof of the splitting theorems from Lorentzian geometry (preprint) http://arxiv.org/abs/2410.12632 2024 N. Gigli, I. Y. Violo: Notes on the Cheeger and Colding version of the Reifenberg theorem for metric spaces Bollettino dell'Unione Matematica Italiana 2024 T. Beran, M. Braun, M. Calisti, N. Gigli, R. J. McCann, A. Ohanyan, F. Rott, C. Sämann: A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes (preprint) http://arxiv.org/abs/2408.15968 2024 L. Gennaioli, N. Gigli, H. C. Zhang, X. P. Zhu: Comments on the regularity of harmonic maps between singular spaces The Journal of Geometric Analysis 2024 M. Braun, N. Gigli, R. J. McCann, A. Ohanyan, C. Sämann: A Lorentzian splitting theorem for continuously differentiable metrics and weights (preprint) http://arxiv.org/abs/2507.06836 2025 N. Gigli: Pills of measure theory on Polish spaces (Lecture Notes) 2025 N. Gigli: Hyperbolic Banach spaces (preprint) http://arxiv.org/abs/2503.10467 2025 N. Gigli: Some examples of use of transfinite induction in analysis (preprint) http://arxiv.org/abs/2512.16973 2025 N. Gigli, F. Rott, M. Zanardini: PDE aspects of the dynamical optimal transport in the Lorentzian setting (preprint) http://arxiv.org/abs/2601.13167 2026 N. Gigli, I. Y. Violo: Mean curvature and sharp Willmore inequalities in metric spaces (preprint) http://arxiv.org/abs/2607.27012 2026 N. Gigli, K. Suzuki, S. Vincini: Pyramids and Extended Metric Measure Spaces (preprint) http://arxiv.org/abs/2607.26626 2026