Full Professor, SISSA

Email: ngigli AT sissa.it

arxiv id: gigli_n_1

Available papers (89):

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• M. Braun - N. Gigli - R. J. McCann - A. Ohanyan - C. Sämann (preprint)
  A Lorentzian splitting theorem for continuously differentiable metrics and weights (2025)
• N. Gigli (Lecture Notes)
  Pills of measure theory on Polish spaces (2025)
• N. Gigli (preprint)
  Hyperbolic Banach spaces (2025)
• 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 - S. Vincini (preprint)
  Stability of the heat flow under convergence in concentration and consequences (2024)
• N. Gigli - L. Tamanini - D. Trevisan (Potential Analysis)
  Viscosity solutions of Hamilton-Jacobi equation in $RCD(K,\infty)$ spaces and applications to large deviations (2024)
• M. Braun - N. Gigli - R. J. McCann - A. Ohanyan - C. Sämann (preprint)
  An elliptic proof of the splitting theorems from Lorentzian geometry (2024)
• N. Gigli - I. Y. Violo (Bollettino dell'Unione Matematica Italiana)
  Notes on the Cheeger and Colding version of the Reifenberg theorem for metric spaces (2024)
• T. Beran - M. Braun - M. Calisti - N. Gigli - R. J. McCann - A. Ohanyan - F. Rott - C. Sämann (preprint)
  A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes (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 - F. Marconi (preprint)
  A general splitting principle on RCD spaces and applications to spaces with positive spectrum (2023)
• N. Gigli (preprint)
  De Giorgi and Gromov working together (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)
• C. Brena - N. Gigli (Journal of Functional Analysis)
  Local vector measures (2022)
• C. Brena - N. Gigli (The Journal of Geometric Analysis)
  Calculus and fine properties of functions of bounded variation on RCD spaces (2022)
• 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)
• E. Caputo - N. Gigli - E. Pasqualetto (Journal für die reine und angewandte Mathematik)
  Parallel transport on non-collapsed $\mathsf{RCD}(K,N)$ spaces (2021)
• N. Gigli - A. Tyulenev (Preprint)
  Korevaar-Schoen's energy on strongly rectifiable spaces (2020)
• S. Di Marino - N. Gigli - A. Pratelli (Rend. Lincei Mat. Appl.)
  Global Lipschitz extension preserving local constants (2020)
• N. Gigli - C. Rigoni (Submitted Paper)
  Partial derivatives in the nonsmooth setting (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 - C. Ketterer - K. Kuwada - S. I. Ohta (preprint)
  Rigidity for the spectral gap on $RCD(K,\infty)$-spaces (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 - A. Mondino - T. Rajala (preprint)
  Euclidean spaces as weak tangents of infinitesimally Hilbertian metric spaces with Ricci curvature bounded below (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)

Seminars:

• 22 oct 2025: Trading linearity for ellipticity - a novel approach to global Lorentzian geometry
• 26 nov 2021: Differentiating in a non-differentiable environment (Colloquio De Giorgi)
• 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

Speaker:

• 20 apr 2026 - 23 apr 2026: Valentia Geometrica 2026: a workshop on Geometric Analysis
• 2 jun 2024 - 8 jun 2024: First Chinese-Italian Workshop on Elliptic PDEs and Variational Problems
• 21 may 2024 - 24 may 2024: Workshop: Synthetic Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension
• 24 jul 2023 - 28 jul 2023: Thematic Session on GMT
• 12 jun 2023 - 16 jun 2023: Calculus of Variations and Geometric Measure Theory
• 30 aug 2021 - 3 sep 2021: Geometric Measure Theory and applications
• 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

Organizer:

• 9 feb 2026 - 13 feb 2026: XXXV Convegno Nazionale di Calcolo delle Variazioni
• 13 oct 2025 - 17 oct 2025: Workshop "Optimal transport and metric geometry across structures"
• 14 jul 2025 - 18 jul 2025: PRIN school on Geometry and Gravity
• 10 feb 2025 - 14 feb 2025: XXXIV Convegno Nazionale di Calcolo delle Variazioni
• 2 dec 2024 - 6 dec 2024: Optimal Transportation and Applications
• 12 feb 2024 - 16 feb 2024: XXXIII Convegno Nazionale di Calcolo delle Variazioni
• 8 may 2023 - 12 may 2023: XXXII Convegno Nazionale di Calcolo delle Variazioni
• 24 oct 2022 - 28 oct 2022: Optimal Transportation and Applications
• 9 may 2022 - 13 may 2022: XXXI Convegno Nazionale di Calcolo delle Variazioni
• 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