WorldCat Identities

Gigli, Nicola

Overview
Works: 16 works in 104 publications in 3 languages and 2,045 library holdings
Roles: Author, Editor, Opponent, Thesis advisor
Publication Timeline
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Most widely held works by Nicola Gigli
Gradient flows : in metric spaces and in the space of probability measures by Luigi Ambrosio( )

48 editions published between 2004 and 2008 in English and German and held by 1,473 WorldCat member libraries worldwide

"This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance."--Jacket
Second order analysis on (P2(M), W2) by Nicola Gigli( Book )

14 editions published between 2011 and 2012 in English and held by 196 WorldCat member libraries worldwide

On the differential structure of metric measure spaces and applications by Nicola Gigli( Book )

12 editions published between 2014 and 2015 in English and held by 135 WorldCat member libraries worldwide

"The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian, ... (iii) To show that on spaces with Ricci curvature bounded from below and dimension bounded from above, the Laplacian of the distance function is always a measure and that this measure has the standard sharp comparison properties. This result requires an additional assumption on the space, which reduces to strict convexity of the norm in the case of smooth Finsler structures and is always satisfied on spaces with linear Laplacian, a situation which is analyzed in detail."--Page v
Measure Theory in Non-Smooth Spaces by Nicola Gigli( )

6 editions published in 2017 in English and Undetermined and held by 113 WorldCat member libraries worldwide

Analysis in singular spaces is becoming an increasingly important area of research, with motivation coming from the calculus of variations, PDEs, geometric analysis, metric geometry and probability theory, just to mention a few areas. In all these fields, the role of measure theory is crucial and an appropriate understanding of the interaction between the relevant measure-theoretic framework and the objects under investigation is important to a successful research.The aim of this book, which gathers contributions from leading specialists with different backgrounds, is that of creating a collection of various aspects of measure theory occurring in recent research with the hope of increasing interactions between different fields. List of contributors: Luigi Ambrosio, Vladimir I. Bogachev, Fabio Cavalletti, Guido De Philippis, Shouhei Honda, Tom Leinster, Christian Léonard, Andrea Marchese, Mark W. Meckes, Filip Rindler, Nageswari Shanmugalingam, Takashi Shioya, and Christina Sormani
Nonsmooth differential geometry : an approach tailored for spaces with Ricci curvature bounded from below by Nicola Gigli( Book )

8 editions published between 2017 and 2018 in English and held by 100 WorldCat member libraries worldwide

"We discuss in which sense general metric measure spaces possess a first order differential structure. Building on this, we then see that on spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting to define Hessian, covariant/exterior derivatives and Ricci curvature."--Page v
Gradient Flows in Metric Spaces and in the Space of Probability Measures by Luigi Ambrosio( )

3 editions published in 2008 in English and held by 10 WorldCat member libraries worldwide

Programma del corso di diritto civile francese by A. M Demante( Book )

in Italian and held by 3 WorldCat member libraries worldwide

Second order analysis on (P2(M), W2)( )

1 edition published in 2011 in English and held by 3 WorldCat member libraries worldwide

Analyse dans les espaces métriques mesurés by Bang-Xian Han( Book )

2 editions published in 2015 in English and held by 2 WorldCat member libraries worldwide

Cette thèse traite de plusieurs sujets d'analyse dans les espaces métriques mesurés, en lien avec le transport optimal et des conditions de courbure-dimension. Nous considérons en particulier les équations de continuité dans ces espaces, du point de vue de fonctionnelles continues sur les espaces de Sobolev, et du point de vue de la dualité avec les courbes absolument continues dans l'espace de Wasserstein. Sous une condition de courbure-dimension, mais sans condition de doublement de mesure ou d'inégalité de Poincaré, nous montrons également l'identification des p-gradients faibles. Nous étudions ensuite les espaces de Sobolev sur le produit tordu de l'ensemble des réels et d'un espace métrique mesuré. En particulier, nous montrons la propriété Sobolev-à-Lipschitz sous une certaine condition de courbure-dimension. Enfin, sous une telle condition et dans le cadre d'une théorie non-lisse de Bakry-Emery, nous obtenons une inégalité améliorée de Bochner et proposons une définition du N-tenseur de Ricci
Gradient Flows : In Metric Spaces and in the Space of Probability Measures by Nicola Gigli( )

2 editions published in 2008 in English and held by 2 WorldCat member libraries worldwide

Devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure, this book focuses on gradient flows in metric spaces. It covers gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance
Heat flow on Alexandrov spaces by Nicola Gigli( )

1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide

Second order analysis on (Ṕ(M),Ẃ) by Nicola Gigli( Book )

1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide

Perimeter as relaxed Minkowski content in metric measure spaces( )

1 edition published in 2017 in English and held by 1 WorldCat member library worldwide

Abstract: In this note we prove that on general metric measure spaces the perimeter is equal to the relaxation of the Minkowski contents w.r.t. convergence in measure
Unidimensional and Evolution Methods for Optimal Transportation by Nicolas Bonnotte( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

Sur une droite, le transport optimal ne pose pas de difficultés. Récemment, ce constat a été utilisé pour traiter des problèmes plus généraux. En effet, on a remarqué qu'une habile désintégration permet souvent de se ramener à la dimension un, ce qui permet d'utiliser les méthodes afférentes pour obtenir un premier résultat, que l'on fait ensuite évoluer pour gagner en précision.Je montre ici l'efficacité de cette approche, en revenant sur deux problèmes déjà résolus partiellement de cette manière, et en complétant la réponse qui en avait été donnée.Le premier problème concerne le calcul de l'application de Yann Brenier. En effet, Guillaume Carlier, Alfred Galichon et Filippo Santambrogio ont prouvé que celle-ci peut être obtenue grâce à une équation différentielle, pour laquelle une condition initiale est donnée par le réarrangement de Knothe--Rosenblatt (lui-même défini via une succession de transformations unidimensionnelles). Ils n'ont cependant traité que des mesures finales discrètes ; j'étends leur résultat aux cas continus. L'équation de Monge--Ampère, une fois dérivée, donne une EDP pour le potentiel de Kantorovitch; mais pour obtenir une condition initiale, il faut utiliser le théorème des fonctions implicites de Nash--Moser.Le chapitre 1 rappelle quelques résultats essentiels de la théorie du transport optimal, et le chapitre 2 est consacré au théorème de Nash--Moser. J'expose ensuite mes propres résultats dans le chapitre 3, et leur implémentation numérique dans le chapitre 4.Enfin, le dernier chapitre est consacré à l'algorithme IDT, développé par François Pitié, Anil C. Kokaram et Rozenn Dahyot. Celui-ci construit une application de transport suffisamment proche de celle de M. Brenier pour convenir à la plupart des applications. Une interprétation en est proposée en termes de flot de gradients dans l'espace des probabilités, avec pour fonctionnelle la distance de Wasserstein projetée. Je démontre aussi l'équivalence de celle-ci avec la distance usuelle de Wasserstein
Entropic Burgers’ equation via a minimizing movement scheme based on the Wasserstein metric by Nicola Gigli( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

As noted by the second author in the context of unstable two-phase porous medium flow, entropy solutions of Burgers’ equation can be recovered from a minimizing movement scheme involving the Wasserstein metric in the limit of vanishing time step size [4]. In this paper, we give a simpler proof by verifying that the anti-derivative is a viscosity solution of the associated Hamilton Jacobi equation
Second Order Analysis on (\mathscr{P}_{2}(M),W_{2}) by Nicola Gigli( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

 
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Gradient flows : in metric spaces and in the space of probability measures Gradient Flows in Metric Spaces and in the Space of Probability Measures Gradient Flows : In Metric Spaces and in the Space of Probability Measures
Covers
Gradient Flows in Metric Spaces and in the Space of Probability MeasuresGradient Flows : In Metric Spaces and in the Space of Probability Measures
Alternative Names
Nicola Gigli Italiaans wiskundige

Nicola Gigli Italian mathematician

Nicola Gigli italienischer Mathematiker

Nicola Gigli matemático italiano

Languages
English (100)

Italian (2)

German (1)