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 A. Figalli, N. Gigli: Local semiconvexity of Kantorovich potentials on non-compact manifolds ESAIM Control Optim. Calc. Var. (Accepted Paper) 2009 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 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. (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 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 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 N. Gigli, A. Mondino: A PDE approach to nonlinear potential theory in metric measure spaces Journal de Math. Pures et Appl. 2012 L. Ambrosio, N. Gigli, G. Savaré: Bakry-Emery curvature-dimension condition and Riemannian Ricci curvature bounds (Submitted Paper) 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, 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 N. Gigli, B. Han: Sobolev Spaces on Warped Products (Submitted Paper) 2015 G. De Philippis, N. Gigli: From volume cone to metric cone in the nonsmooth setting Geom. Funct. Anal. (Accepted Paper) 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 N. Gigli, E. Pasqualetto: Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces (Submitted Paper) 2016 L. Ambrosio, S. Di Marino, N. Gigli: Perimeter as relaxed Minkowski content in metric measure spaces Nonlinear Analysis: Theory, Methods & Applications (Submitted Paper) Vol. 153, p. 78-88, 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) 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) 2018 N. Gigli, E. Pasqualetto: On the notion of parallel transport on $\sf RCD$ spaces (preprint) 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: Riemann curvature tensor on ${\sf RCD}$ spaces and possible applications (preprint) 2019 C. Debin, N. Gigli, E. Pasqualetto: Quasi-continuous vector fields on RCD spaces (preprint) 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) 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 E. Caputo, N. Gigli, E. Pasqualetto: Parallel transport on non-collapsed $\mathsf{RCD}(K,N)$ spaces (preprint) 2021 N. Gigli, F. Nobili: A differential perspective on Gradient Flows on ${\sf CAT}()$-spaces and applications J. Geom. Anal. 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) (Accepted Paper) 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: Calculus and fine properties of functions of bounded variation on RCD spaces (preprint) 2022 N. Gigli: On the regularity of harmonic maps from ${\sf RCD}(K,N)$ to ${\sf CAT}(0)$ spaces and related results (preprint) 2022 N. Gigli, D. Lui, E. Pasqualetto: Duals and pullbacks of normed modules (preprint) 2022 N. Gigli, F. Nobili: A first-order condition for the independence on $p$ of weak gradients J. Funct. Anal. 2022 N. Gigli, L. Tamanini, D. Trevisan: Viscosity solutions of Hamilton-Jacobi equation in $RCD(K,\infty)$ spaces and applications to large deviations (preprint) 2022 C. Brena, N. Gigli: Local vector measures (preprint) 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, A. Mondino, D. Semola: On the notion of Laplacian bounds on $\mathrm{RCD}$ spaces and applications Proc. Amer. Math. Soc. (Accepted Paper) p. 12, 2023 C. Brena, N. Gigli: About the general chain rule for functions of bounded variation (preprint) 2023 C. Brena, N. Gigli: Fine representation of Hessian of convex functions and Ricci tensor on RCD spaces (preprint) 2023