[gigli]

Full Professor, SISSA

**Email:** *nicolagigli AT googlemail.com*

**arxiv id:** gigli_n_1

- N. Gigli - I. Y. Violo (preprint)

Monotonicity formulas for harmonic functions in ${\rm RCD}(0,N)$ spaces (2021) - N. Gigli - A. Tyulenev (Preprint)

Korevaar-Schoen's energy on strongly rectifiable spaces (2020) - S. Di Marino - N. Gigli - A. Pratelli (Accepted Paper:
*Rend. Lincei Mat. Appl.*)

Global Lipschitz extension preserving local constants (2020) - N. Gigli - C. Rigoni (Submitted Paper)

Partial derivatives in the nonsmooth setting (2020) - N. Gigli - F. Nobili (Preprint)

A differential perspective on Gradient Flows on ${\sf CAT}(κ)$-spaces and applications (2020) - F. Cavalletti - N. Gigli - F. Santarcangelo (Accepted Paper:
*Annales de la faculté des sciences de Toulouse*)

Displacement convexity of Entropy and the distance cost Optimal Transportation (2020) - N. Gigli (preprint)

Riemann curvature tensor on ${\sf RCD}$ spaces and possible applications (2019) - C. Debin - N. Gigli - E. Pasqualetto (preprint)

Quasi-continuous vector fields on RCD spaces (2019) - N. Gigli - A. Tyulenev (Preprint)

Korevaar-Schoen's directional energy and Ambrosio's regular Lagrangian flows (2019) - N. Gigli - E. Pasqualetto (Preprint)

Differential structure associated to axiomatic Sobolev spaces (2018) - N. Gigli - E. Pasqualetto - E. Soultanis (Submitted Paper)

Differential of metric valued Sobolev maps (2018) - S. Di Marino - N. Gigli - E. Pasqualetto - E. Soultanis (Submitted Paper)

Infinitesimal Hilbertianity of locally ${\rm Cat}(\kappa)$-spaces (2018) - N. Gigli - L. Tamanini (Accepted Paper:
*J. Eur. Math. Soc. (JEMS)*)

Second order differentiation formula on $RCD^*(K,N)$ spaces (2018) - N. Gigli - L. Tamanini (
*Probab. Theory Related Fields*)

Benamou-Brenier and duality formulas for the entropic cost on $RCD^*(K,N)$ spaces (2018) - N. Gigli - E. Pasqualetto (preprint)

On the notion of parallel transport on $\sf RCD$ spaces (2018) - N. Gigli - L. Tamanini (Submitted Paper)

Second order differentiation formula on compact $RCD^*(K,N)$ spaces (2017) - N. Gigli (Preprint)

Lecture notes on differential calculus on RCD spaces (2017) - N. Gigli - C. Rigoni (Submitted Paper)

Recognizing the flat torus among $RCD^*(0,N)$ spaces via the study of the first cohomology group (2017) - N. Gigli - C. Rigoni (Preprint)

A note about the strong maximum principle on $RCD$ spaces (2017) - N. Gigli - L. Tamanini (Proceedings:
*Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.*)

Second order differentiation formula on $RCD(K,N)$ spaces (2017) - G. De Philippis - N. Gigli (Preprint)

Non-collapsed spaces with Ricci curvature bounded from below (2017) - N. Gigli - E. Pasqualetto (Preprint)

Behaviour of the reference measure on $\sf RCD$ spaces under charts (2016) - N. Gigli - B. Han (
*Journal of Functional Analysis*)

Independence on p of weak upper gradients on RCD spaces (2016) - N. Gigli - E. Pasqualetto (Submitted Paper)

Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces (2016) - L. Ambrosio - N. Gigli - S. Di Marino (Submitted Paper:
*Nonlinear Analysis: Theory, Methods & Applications*)

Perimeter as relaxed Minkowski content in metric measure spaces (2016) - N. Gigli - B. Han (
*Calculus of Variations and Partial Differential Equations*)

The continuity equation on metric measure spaces (2015) - N. Gigli - B. Han (Submitted Paper)

Sobolev Spaces on Warped Products (2015) - N. Gigli - G. De Philippis (Accepted Paper:
*Geom. Funct. Anal.*)

From volume cone to metric cone in the nonsmooth setting (2015) - N. Gigli - S. J. N. Mosconi (Preprint)

The abstract Lewy Stampacchia inequality and applications (2014) - N. Gigli - C. Mantegazza (
*Advances in Math.*)

A Flow Tangent to the Ricci Flow via Heat Kernels and Mass Transport (2014) - N. Gigli (Preprint)

Nonsmooth differential geometry - An approach tailored for spaces with Ricci curvature bounded from below (2014) - N. Gigli (Submitted Paper)

The splitting theorem in non-smooth context (2013) - N. Gigli - T. Rajala - K. T. Sturm (Submitted Paper)

Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below (2013) - N. Gigli (Submitted Paper)

An overview on the proof of the splitting theorem in non-smooth context (2013) - N. Gigli - A. Mondino - T. Rajala (Accepted Paper:
*J. Reine Angew. Math.*)

Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below (2013) - N. Gigli - A. Mondino - G. Savaré (Accepted Paper:
*Proceedings of the London Mathematical Society*)

Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows (2013) - N. Gigli (Preprint)

On the relation between the curvature-dimension condition and the Bochner inequality (2012) - L. Ambrosio - N. Gigli - G. Savaré (Preprint)

Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case (2012) - N. Gigli - J. Maas (Submitted Paper)

Gromov-Hausdorff convergence of discrete transportation metrics (2012) - N. Gigli - S. J. N. Mosconi (Submitted Paper)

The Abresch-Gromoll inequality in a non-smooth setting (2012) - L. Ambrosio - N. Gigli - A. Mondino - T. Rajala (Accepted Paper:
*Transactions of the AMS*)

Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure (2012) - N. Gigli (Preprint)

On the differential structure of metric measure spaces and applications (2012) - N. Gigli - A. Mondino (
*Journal de Math. Pures et Appl.*)

A PDE approach to nonlinear potential theory in metric measure spaces (2012) - L. Ambrosio - N. Gigli - G. Savaré (Submitted Paper)

Bakry-Emery curvature-dimension condition and Riemannian Ricci curvature bounds (2012) - N. Gigli - S. J. N. Mosconi (Accepted at Bullettin des Sciences Mathematiques)

A variational approach to the Navier-Stokes equations (2011) - L. Ambrosio - N. Gigli

A user's guide to optimal transport (2011) - N. Gigli (Accepted at GAFA)

Optimal maps in non branching spaces with Ricci curvature bounded from below (2011) - L. Ambrosio - N. Gigli - G. Savaré (Submitted Paper)

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below (2011) - N. Gigli (Memoire HDR)

Geometric and analytic properties of some non smooth structures (2011) - L. Ambrosio - N. Gigli - G. Savaré (Submitted Paper)

Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces (2011) - N. Gigli - M. Ledoux (Accepted Paper: DCDS-A)

From log Sobolev to Talagrand: a quick proof (2011) - L. Ambrosio - N. Gigli - G. Savaré (Submitted Paper)

Metric measure spaces with Riemannian Ricci curvature bounded from below (2011) - N. Gigli - F. Otto (Accepted at Calc.Var and PDE)

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric (2010) - N. Gigli - K. Kuwada - S. I. Ohta (Accepted at CPAM)

Heat Flow on Alexandrov spaces (2010) - N. Gigli - S. I. Ohta (Accepted Paper:
*Canad. Math. Bull.*)

First variation formula in Wasserstein spaces over compact Alexandrov spaces (2010) - N. Gigli (Accepted Paper:
*Calc. Var. Part. Diff. Eq.*)

On the Heat flow on metric measure spaces: existence, uniqueness and stability (2010) - A. Figalli - N. Gigli (Accepted Paper:
*ESAIM Control Optim. Calc. Var.*)

Local semiconvexity of Kantorovich potentials on non-compact manifolds (2009) - N. Gigli (Accepted Paper:
*Rendiconti di matematica*)

On the weak closure of convex sets of Probability measures (2009) - N. Gigli (Accepted Paper:
*Meth. Appl. of Anal.*)

On the inverse implication of Brenier-McCann theorems and the structure of $(P_2(M),W_2)$ (2009) - A. Figalli - N. Gigli (Accepted Paper:
*J. Math. Pures Appl.*)

A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions (2009) - N. Gigli (Accepted Paper:
*Memoirs of the American Mathematical Society*)

Second order analysis on (P_2(M),W_2) (2009) - N. Gigli (Ph.D. Thesis)

On the geometry of the space of probability measures endowed with the quadratic optimal transport distance (2008) - L. Ambrosio - N. Gigli (Accepted Paper:
*Methods and Applications of Analysis*)

Construction of the parallel transport in the Wasserstein space (2008) - N. Gigli (Accepted Paper:
*Proceedings of the Edinburgh Mathematical Society*)

On Hölder continuity in time of the optimal transport map towards measures along a curve (2008) - L. Ambrosio - N. Gigli - G. Savaré (Accepted Paper)

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space (2003)

*18 feb 2021:*Curvature and Metric Geometry*3 apr 2003:*Sulle equazioni del primo ordine con coefficienti in spazi di Sobolev. I I*27 mar 2003:*Sulle equazioni del primo ordine con coefficienti in spazi di Sobolev, I

*15 dec 2019 - 18 dec 2019:*Junior Math Days 2019*1 apr 2019 - 5 apr 2019:*Optimal Transport and Geometric Analysis*14 jan 2019 - 17 jan 2019:*Alessio Figalli, Fields medallist 2018*16 dec 2018 - 19 dec 2018:*Junior Math Days - second edition*3 sep 2018 - 6 sep 2018:*Meeting on Applied Mathematics and Calculus of Variations*19 sep 2016 - 23 sep 2016:*A Mathematical Tribute to Ennio De Giorgi*11 jul 2016 - 15 jul 2016:*School in Geometric Analysis: "Geometric Analysis on Riemannian and singular metric measure spaces"*23 feb 2015 - 27 feb 2015:*Winter School & Workshop: New developments in Optimal Transport, Geometry and Analysis*27 oct 2014 - 31 oct 2014:*ERC Workshop on Optimal Transportation and Applications*10 jan 2014 - 10 jan 2014:*A Geometry Day in Como*5 nov 2012 - 9 nov 2012:*ERC Workshop on Optimal Transportation and Applications*18 jun 2012 - 22 jun 2012:*Optimal Transport (to) Orsay*7 may 2012 - 11 may 2012:*ERC Summer School "Analysis and Geometry in Metric Measure Spaces''*10 oct 2011 - 14 oct 2011:*ERC Workshop on Geometric Analysis on sub-Riemannian and Metric Spaces

*27 jan 2020 - 1 feb 2020:*Calculus of Variations and Applications (on the occasion of Gianni Dal Maso's birthday)*12 nov 2018 - 16 nov 2018:*Optimal Transport and Applications*9 jun 2014 - 13 jun 2014:*Analysis and Geometry on Singular Spaces