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
N. Gigli, L. Tamanini:
Second order differentiation formula on $RCD(K,N)$ spaces
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. (Proceedings) 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, L. Tamanini:
Second order differentiation formula on $RCD^*(K,N)$ spaces
J. Eur. Math. Soc. (JEMS) (Accepted Paper) 2018
N. Gigli, L. Tamanini:
Benamou-Brenier and duality formulas for the entropic cost on $RCD^*(K,N)$ spaces
Probab. Theory Related Fields 2018
N. Gigli, E. Pasqualetto:
On the notion of parallel transport on $\sf RCD$ spaces
(preprint) 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. (Accepted Paper) 2020
N. Gigli, C. Rigoni:
Partial derivatives in the nonsmooth setting
(Submitted Paper) 2020
N. Gigli, F. Nobili:
A differential perspective on Gradient Flows on ${\sf CAT}()$-spaces and applications
(Preprint) 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, I. Y. Violo:
Monotonicity formulas for harmonic functions in ${\rm RCD}(0,N)$ spaces
(preprint) 2021