Gradient Flows PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Gradient Flows PDF full book. Access full book title Gradient Flows.
| Author | : Luigi Ambrosio |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 334 |
| Release | : 2008-10-29 |
| Genre | : Mathematics |
| ISBN | : 376438722X |
Download Gradient Flows Book in PDF, ePub and Kindle
The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
| Author | : Luigi Ambrosio |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 330 |
| Release | : 2006-03-30 |
| Genre | : Mathematics |
| ISBN | : 3764373091 |
Download Gradient Flows Book in PDF, ePub and Kindle
This book is devoted to a theory of gradient ?ows in spaces which are not nec- sarily endowed with a natural linear or di?erentiable structure. It is made of two parts, the ?rst one concerning gradient ?ows in metric spaces and the second one 2 1 devoted to gradient ?ows in the L -Wasserstein space of probability measures on p a separable Hilbert space X (we consider the L -Wasserstein distance, p? (1,?), as well). The two parts have some connections, due to the fact that the Wasserstein space of probability measures provides an important model to which the “metric” theory applies, but the book is conceived in such a way that the two parts can be read independently, the ?rst one by the reader more interested to Non-Smooth Analysis and Analysis in Metric Spaces, and the second one by the reader more oriented to theapplications in Partial Di?erential Equations, Measure Theory and Probability.
| Author | : Katz Gabriel |
| Publisher | : World Scientific |
| Total Pages | : 516 |
| Release | : 2019-08-21 |
| Genre | : Mathematics |
| ISBN | : 9814719684 |
Download Morse Theory Of Gradient Flows, Concavity And Complexity On Manifolds With Boundary Book in PDF, ePub and Kindle
This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of the Singularity Theory of smooth maps.The geometric and combinatorial structures, arising from the interactions of vector flows with the boundary of the manifold, are surprisingly rich. This geometric setting leads organically to many encounters with Singularity Theory, Combinatorics, Differential Topology, Differential Geometry, Dynamical Systems, and especially with the boundary value problems for ordinary differential equations. This diversity of connections animates the book and is the main motivation behind it.The book is divided into two parts. The first part describes the flows in three dimensions. It is more pictorial in nature. The second part deals with the multi-dimensional flows, and thus is more analytical. Each of the nine chapters starts with a description of its purpose and main results. This organization provides the reader with independent entrances into different chapters.
| Author | : Anthony Bloch |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 172 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 9780821871362 |
Download Hamiltonian and Gradient Flows, Algorithms, and Control Book in PDF, ePub and Kindle
This is the proceedings of a conference held at the Fields Insitute and designed to bring together traditionally disparate fields of mathematical research. On such key interraction occurs between dynamical systems and algorithms. This volume explores many such interractions as well as related work in optimal control and partial differential equations.
| Author | : Alessio Figalli |
| Publisher | : European Mathematical Society |
| Total Pages | : 0 |
| Release | : 2023-05-15 |
| Genre | : Mathematics |
| ISBN | : 3985470502 |
Download An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows Book in PDF, ePub and Kindle
This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject. The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Otto's calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given. Suitable for a course at the graduate level, the book also includes an appendix with a series of exercises along with their solutions. The second edition contains a number of additions, such as a new section on the Brunn–Minkowski inequality, new exercises, and various corrections throughout the text.
| Author | : Karl-Theodor Sturm |
| Publisher | : American Mathematical Society |
| Total Pages | : 124 |
| Release | : 2023-11-27 |
| Genre | : Mathematics |
| ISBN | : 1470466961 |
Download The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces Book in PDF, ePub and Kindle
View the abstract.
| Author | : Luigi Ambrosio |
| Publisher | : Springer Nature |
| Total Pages | : 250 |
| Release | : 2021-07-22 |
| Genre | : Mathematics |
| ISBN | : 3030721620 |
Download Lectures on Optimal Transport Book in PDF, ePub and Kindle
This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations.
| Author | : Ben Andrews |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 306 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 3642162851 |
Download The Ricci Flow in Riemannian Geometry Book in PDF, ePub and Kindle
This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.
| Author | : Yann Ollivier |
| Publisher | : Cambridge University Press |
| Total Pages | : 317 |
| Release | : 2014-08-07 |
| Genre | : Mathematics |
| ISBN | : 1139993623 |
Download Optimal Transport Book in PDF, ePub and Kindle
The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory and Applications' held at the Fourier Institute in Grenoble. The event brought together mathematicians from pure and applied mathematics, astrophysics, economics and computer science. Part I of this book is devoted to introductory lecture notes accessible to graduate students, while Part II contains research papers. Together, they represent a valuable resource on both fundamental and advanced aspects of optimal transportation, its applications, and its interactions with analysis, geometry, PDE and probability, urban planning and economics. Topics covered include Ricci flow, the Euler equations, functional inequalities, curvature-dimension conditions, and traffic congestion.
| Author | : Anatole Katok |
| Publisher | : Cambridge University Press |
| Total Pages | : 828 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 9780521575577 |
Download Introduction to the Modern Theory of Dynamical Systems Book in PDF, ePub and Kindle
This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.
