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2014

Gigli N, Mosconi S. The Abresch-Gromoll inequality in a non-smooth setting. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS [Internet]. 2014 ;34:1481–1509. Available from: https://arxiv.org/abs/1209.3813

Ambrosio L, Gigli N, Savaré G. Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below. INVENTIONES MATHEMATICAE [Internet]. 2014 ;195:289–391. Available from: https://arxiv.org/abs/1106.2090

Gigli N, Mantegazza C. A flow tangent to the Ricci flow via heat kernels and mass transport. ADVANCES IN MATHEMATICS [Internet]. 2014 ;250:74–104. Available from: https://arxiv.org/abs/1208.5815

Ambrosio L, Gigli N, Savaré G. Metric measure spaces with Riemannian Ricci curvature bounded from below. DUKE MATHEMATICAL JOURNAL [Internet]. 2014 ;163:1405–1490. Available from: https://arxiv.org/abs/1109.0222

Gigli N. An overview of the proof of the splitting theorem in spaces with non-negative ricci curvature. ANALYSIS AND GEOMETRY IN METRIC SPACES [Internet]. 2014 ;2:169–213. Available from: https://arxiv.org/abs/1305.4854

2013

Ambrosio L, Gigli N, Savaré G. Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces. REVISTA MATEMATICA IBEROAMERICANA [Internet]. 2013 ;29:969–996. Available from: https://arxiv.org/abs/1111.3730

Gigli N, Otto F. Entropic Burgers’ equation via a minimizing movement scheme based on the Wasserstein metric. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS [Internet]. 2013 ;47:181–206. Available from: http://cvgmt.sns.it/paper/143/

Gigli N, Ledoux M. From log Sobolev to Talagrand: a quick proof. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. 2013 ;33:1927–1935.

Gigli N, Mass J. Gromov-Hausdorff convergence of discrete transportation metrics. SIAM JOURNAL ON MATHEMATICAL ANALYSIS [Internet]. 2013 ;45:879–899. Available from: http://cdsads.u-strasbg.fr/abs/2012arXiv1207.6501G

Ambrosio L, Gigli N, Savaré G. Heat flow and calculus on metric measure spaces with ricci curvature bounded below—The compact case. In: Analysis and numerics of partial differential equations. Vol. 4. Analysis and numerics of partial differential equations. Milano: Springer Italia; 2013. pp. 63–115. Available from: http://www.springer.com/la/book/9788847025912

Gigli N, Kuwada K, Shin IOhta. Heat Flow on Alexandrov spaces. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS [Internet]. 2013 ;66:307–331. Available from: https://arxiv.org/abs/1008.1319

Gigli N, Mondino A. A PDE approach to nonlinear potential theory. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. 2013 ;100:505–534.

Gigli N. The splitting theorem in non-smooth context.; 2013. Available from: http://preprints.sissa.it/handle/1963/35306

Ambrosio L, Gigli N. A user's guide to optimal transport. In: Modelling and Optimisation of Flows on Networks : Cetraro, Italy 2009. Vol. 2062. Modelling and Optimisation of Flows on Networks : Cetraro, Italy 2009. HEIDELBERG, DORDRECHT, LONDON: Springer-Verlag BERLIN-HEIDELBERG; 2013. pp. 1–155. Available from: https://link.springer.com/book/10.1007%2F978-3-642-32160-3

2012

Gigli N, Ohta Sichi. First variation formula in Wasserstein spaces over compact Alexandrov spaces. CANADIAN MATHEMATICAL BULLETIN. 2012 ;55:723–735.

Gigli N. Optimal maps in non branching spaces with Ricci curvature bounded from below. GEOMETRIC AND FUNCTIONAL ANALYSIS. 2012 ;22:990–999.

Gigli N. Second Order Analysis on (P-2(M), W-2). MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY [Internet]. 2012 ;216:1–173. Available from: http://www.ams.org/books/memo/1018/

Gigli N, Mosconi S. A variational approach to the Navier-Stokes equations. BULLETIN DES SCIENCES MATHEMATIQUES. 2012 ;136:256–276.

2011

Gigli N. On Holder continuity in time of the optimal transport map towards measures along a curve. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY. 2011 ;54:401–409.

Gigli N. On the inverse implication of Brenier-McCann theorems and the structure of P_2(M). METHODS AND APPLICATIONS OF ANALYSIS [Internet]. 2011 ;18:127–158. Available from: http://intlpress.com/site/pub/pages/journals/items/maa/content/vols/0018/0002/index.html

Gigli N, Figalli A. Local semiconvexity of Kantorovich potentials on non-compact manifolds. ESAIM. COCV. 2011 ;17:648–653.

Gigli N. Propriétés géométriques et analytiques de certaines structures non lisses. [Internet]. 2011 . Available from: http://tel.archives-ouvertes.fr/tel-00769381

2010

Gigli N. On the heat flow on metric measure spaces: Existence, uniqueness and stability. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS [Internet]. 2010 ;39:101–120. Available from: https://doi.org/10.1007/s00526-009-0303-9

Figalli A, Gigli N. A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES [Internet]. 2010 ;94:107–130. Available from: https://doi.org/10.1016/j.matpur.2009.11.005

2009

Gigli N. Weak closure of geodesically convex subsets of Probability measures. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO [Internet]. 2009 . Available from: http://cvgmt.sns.it/paper/599/

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