Metric Measure Geometry PDF Download
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| Author | : Takashi Shioya |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2016 |
| Genre | : Geometry, Differential |
| ISBN | : 9783037191583 |
Download Metric Measure Geometry Book in PDF, ePub and Kindle
This book studies a new theory of metric geometry on metric measure spaces. The theory was originally developed by M. Gromov in his book Metric Structures for Riemannian and Non-Riemannian Spaces and based on the idea of the concentration of measure phenomenon by Levy and Milman. A central theme in this book is the study of the observable distance between metric measure spaces, defined by the difference between 1-Lipschitz functions on one space and those on the other. The topology on the set of metric measure spaces induced by the observable distance function is weaker than the measured Gromov-Hausdorff topology and allows the author to investigate a sequence of Riemannian manifolds with unbounded dimensions. One of the main parts of this presentation is the discussion of a natural compactification of the completion of the space of metric measure spaces. The stability of the curvature-dimension condition is also discussed.
| Author | : Galia Devora Dafni |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 241 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 0821894188 |
Download Analysis and Geometry of Metric Measure Spaces Book in PDF, ePub and Kindle
Contains lecture notes from most of the courses presented at the 50th anniversary edition of the Seminaire de Mathematiques Superieure in Montreal. This 2011 summer school was devoted to the analysis and geometry of metric measure spaces, and featured much interplay between this subject and the emergent topic of optimal transportation.
| Author | : Richard S. Millman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 394 |
| Release | : 1993-05-07 |
| Genre | : Mathematics |
| ISBN | : 9780387974125 |
Download Geometry Book in PDF, ePub and Kindle
Geometry: A Metric Approach with Models, imparts a real feeling for Euclidean and non-Euclidean (in particular, hyperbolic) geometry. Intended as a rigorous first course, the book introduces and develops the various axioms slowly, and then, in a departure from other texts, continually illustrates the major definitions and axioms with two or three models, enabling the reader to picture the idea more clearly. The second edition has been expanded to include a selection of expository exercises. Additionally, the authors have designed software with computational problems to accompany the text. This software may be obtained from George Parker.
| Author | : Dmitri Burago |
| Publisher | : American Mathematical Society |
| Total Pages | : 415 |
| Release | : 2022-01-27 |
| Genre | : Mathematics |
| ISBN | : 1470468530 |
Download A Course in Metric Geometry Book in PDF, ePub and Kindle
“Metric geometry” is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Carathéodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with “easy-to-touch” mathematical objects using “easy-to-visualize” methods. The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.
| Author | : Fabrice Baudoin |
| Publisher | : Springer Nature |
| Total Pages | : 312 |
| Release | : 2022-02-04 |
| Genre | : Mathematics |
| ISBN | : 3030841413 |
Download New Trends on Analysis and Geometry in Metric Spaces Book in PDF, ePub and Kindle
This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. Authored by leading experts in their fields, the lectures present different approaches to research topics with the common background of a relevant underlying, usually non-Riemannian, geometric structure. In particular, the topics covered concern differentiation and functions of bounded variation in metric spaces, Sobolev spaces, and differential geometry in the so-called Carnot–Carathéodory spaces. The text is based on lectures presented at the 10th School on "Analysis and Geometry in Metric Spaces" held in Levico Terme (TN), Italy, in collaboration with the University of Trento, Fondazione Bruno Kessler and CIME, Italy. The book is addressed to both graduate students and researchers.
| Author | : Stephanie Alexander |
| Publisher | : Springer |
| Total Pages | : 88 |
| Release | : 2019-05-08 |
| Genre | : Mathematics |
| ISBN | : 3030053121 |
Download An Invitation to Alexandrov Geometry Book in PDF, ePub and Kindle
Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.
| Author | : Gerald A. Edgar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 252 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1475741340 |
Download Measure, Topology, and Fractal Geometry Book in PDF, ePub and Kindle
From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so many: 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1
| Author | : James J Yeh |
| Publisher | : World Scientific |
| Total Pages | : 308 |
| Release | : 2019-11-18 |
| Genre | : Mathematics |
| ISBN | : 9813200421 |
Download Metric In Measure Spaces Book in PDF, ePub and Kindle
Measure and metric are two fundamental concepts in measuring the size of a mathematical object. Yet there has been no systematic investigation of this relation. The book closes this gap.
| Author | : Michel Marie Deza |
| Publisher | : Springer |
| Total Pages | : 580 |
| Release | : 2009-11-12 |
| Genre | : Mathematics |
| ISBN | : 3642042953 |
Download Geometry of Cuts and Metrics Book in PDF, ePub and Kindle
Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields [...]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [...] The longer one works with it, the more beautiful it becomes." Optima 56, 1997.
| Author | : Juha Heinonen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 149 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461301319 |
Download Lectures on Analysis on Metric Spaces Book in PDF, ePub and Kindle
The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is recent and appears for the first time in book format.
