Full Professor,
SISSA
Email: nicolagigli AT googlemail.com
arxiv id: gigli_n_1
Available papers (80):
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- N. Gigli - A. Mondino - D. Semola (Proc. Amer. Math. Soc.)
On the notion of Laplacian bounds on $\mathrm{RCD}$ spaces and applications (2024)
- L. Gennaioli - N. Gigli - H. C. Zhang - X. P. Zhu (preprint)
Comments on the regularity of harmonic maps between singular spaces (2024)
- N. Gigli - I. Y. Violo (preprint)
Notes on the Cheeger and Colding version of the Reifenberg theorem for metric spaces (2024)
- N. Gigli - S. Vincini (preprint)
Stability of the heat flow under convergence in concentration and
consequences (2024)
- C. Brena - N. Gigli (Potential Anal.)
Fine representation of Hessian of convex functions and Ricci tensor on RCD spaces (2023)
- C. Brena - N. Gigli (Nonlinear Analysis)
About the general chain rule for functions of bounded variation (2023)
- N. Gigli - D. Lučić - E. Pasqualetto (preprint)
Duals and pullbacks of normed modules (2022)
- N. Gigli - F. Nobili (J. Funct. Anal.)
A first-order condition for the independence on $p$ of weak gradients (2022)
- L. Gennaioli - N. Gigli (Canadian Mathematical Bulletin)
A note about charts built by Eriksson-Bique and Soultanis on metric measure spaces (2022)
- N. Gigli (preprint)
On the regularity of harmonic maps from ${\sf RCD}(K,N)$ to ${\sf
CAT}(0)$ spaces and related results (2022)
- N. Gigli - L. Tamanini - D. Trevisan (preprint)
Viscosity solutions of Hamilton-Jacobi equation in $RCD(K,\infty)$ spaces and applications to large deviations (2022)
- C. Brena - N. Gigli (The Journal of Geometric Analysis)
Calculus and fine properties of functions of bounded variation on RCD spaces (2022)
- C. Brena - N. Gigli (Journal of Functional Analysis)
Local vector measures (2022)
- E. Caputo - N. Gigli - E. Pasqualetto (preprint)
Parallel transport on non-collapsed $\mathsf{RCD}(K,N)$ spaces (2021)
- N. Gigli - F. Nobili (J. Geom. Anal.)
A differential perspective on Gradient Flows on ${\sf CAT}(κ)$-spaces and applications (2021)
- N. Gigli - I. Y. Violo (The Journal of Geometric Analysis)
Monotonicity formulas for harmonic functions in ${\rm RCD}(0,N)$ spaces (2021)
- N. Gigli - L. Tamanini (J. Eur. Math. Soc. (JEMS))
Second order differentiation formula on $RCD^*(K,N)$ spaces (2021)
- C. Brena - N. Gigli - S. Honda - X. Zhu (J. Reine Angew. Math. (Crelle's Journal))
Weakly non-collapsed RCD spaces are strongly non-collapsed (2021)
- N. Gigli - A. Tyulenev (Preprint)
Korevaar-Schoen's energy on strongly rectifiable spaces (2020)
- N. Gigli - C. Rigoni (Submitted Paper)
Partial derivatives in the nonsmooth setting (2020)
- S. Di Marino - N. Gigli - A. Pratelli (Rend. Lincei Mat. Appl.)
Global Lipschitz extension preserving local constants (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 - L. Tamanini (Probab. Theory Related Fields)
Benamou-Brenier and duality formulas for the entropic cost on $RCD^*(K,N)$ spaces (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 - E. Pasqualetto (preprint)
On the notion of parallel transport on $\sf RCD$ spaces (2018)
- N. Gigli - L. Tamanini (Proceedings: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.)
Second order differentiation formula on $RCD(K,N)$ spaces (2018)
- N. Gigli - B. Han (Journal of Functional Analysis)
Sobolev Spaces on Warped Products (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)
- 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)
- 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 - E. Pasqualetto (Submitted Paper)
Equivalence of two different notions of tangent bundle on rectifiable 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 - 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)
- L. Ambrosio - N. Gigli - G. Savaré (Submitted Paper)
Bakry-Emery curvature-dimension condition and Riemannian Ricci curvature bounds (2012)
- N. Gigli - A. Mondino (Journal de Math. Pures et Appl.)
A PDE approach to nonlinear potential theory in metric measure spaces (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)
- A. Figalli - N. Gigli (ESAIM Control Optim. Calc. Var.)
Local semiconvexity of Kantorovich potentials on non-compact manifolds (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 (J. Math. Pures Appl.)
A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions (2010)
- 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)
- 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)
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