Gradient Flows PDF Download
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| Author | : Luigi Ambrosio |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 333 |
| 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 | : 166 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 0821802550 |
Download Hamiltonian and Gradient Flows, Algorithms and Control Book in PDF, ePub and Kindle
This volume brings together ideas from several areas of mathematics that have traditionally been rather disparate. The conference at the Fields Institute which gave rise to these proceedings was intended to enourage such connections. One of the key interactions occurs between dynamical systems and algorithms, one example being the by now classic observation that the QR algorithm for diagonalizing matrices may be viewed as the time-1 map of the Toda lattice flow. Another link occurs with interior point methods for linear programming, where certain smooth flows associated with such programming problems have proved valuable in the analysis of the corresponding discrete problems. More recently, other smooth flows have been introduced which carry out discrete computations (such as sorting sets of numbers) and which solve certain least squares problems. Another interesting facet of the flows described here is that they often have a dual Hamiltonian and gradient structure, both of which turn out to be useful in analysing and designing algorithms for solving optimization problems. This volume explores many of these interactions, as well as related work in optimal control and partial differential equations.
| 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
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| 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 | : 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 | : 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 | : Alexander Krasnitz |
| Publisher | : World Scientific |
| Total Pages | : 238 |
| Release | : 1999-08-13 |
| Genre | : |
| ISBN | : 9814543578 |
Download Exact Renormalization Group, The - Proceedings Of The Workshop Book in PDF, ePub and Kindle
The subject of the exact renormalization group started from pioneering work by Wegner and Houghton in the early seventies and, a decade later, by Polchinski, who formulated the Wilson renormalization group for field theory. In the past decade considerable progress has been made in this field, which includes the development of alternative formulations of the approach and of powerful techniques for solving the exact renormalization group equations, as well as widening of the scope of the exact renormalization group method to include fermions and gauge fields. In particular, two very recent results, namely the manifestly gauge-invariant formulation of the exact renormalization group equation and the proof of the c-theorem in four dimensions, are presented in this volume.
| Author | : Liviu I. Nicolaescu |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 145 |
| Release | : 2010-10-07 |
| Genre | : Mathematics |
| ISBN | : 0821848704 |
Download Tame Flows Book in PDF, ePub and Kindle
The tame flows are ``nice'' flows on ``nice'' spaces. The nice (tame) sets are the pfaffian sets introduced by Khovanski, and a flow $\Phi: \mathbb{R}\times X\rightarrow X$ on pfaffian set $X$ is tame if the graph of $\Phi$ is a pfaffian subset of $\mathbb{R}\times X\times X$. Any compact tame set admits plenty tame flows. The author proves that the flow determined by the gradient of a generic real analytic function with respect to a generic real analytic metric is tame.
