METRIC STRUCTURES FOR RIEMANNIAN AND NON RIEMANNIAN SPACES MODERN BIRKHAUSER CLASSICS

Download Metric Structures For Riemannian And Non Riemannian Spaces Modern Birkhauser Classics ebook PDF or Read Online books in PDF, EPUB, and Mobi Format. Click Download or Read Online button to METRIC STRUCTURES FOR RIEMANNIAN AND NON RIEMANNIAN SPACES MODERN BIRKHAUSER CLASSICS book pdf for free now.

Metric Structures For Riemannian And Non Riemannian Spaces

Author : Mikhail Gromov
ISBN : 9780817645830
Genre : Mathematics
File Size : 49.88 MB
Format : PDF, ePub, Mobi
Download : 744
Read : 323

This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.
Category: Mathematics

Metric Structures For Riemannian And Non Riemannian Spaces

Author : Mikhail Gromov
ISBN : 0817638989
Genre : Mathematics
File Size : 66.27 MB
Format : PDF, ePub, Docs
Download : 622
Read : 196

This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.
Category: Mathematics

A Course In Metric Geometry

Author : Dmitri Burago
ISBN : 9780821821299
Genre : Mathematics
File Size : 49.67 MB
Format : PDF, Mobi
Download : 887
Read : 1258

``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-Caratheodory 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.
Category: Mathematics

Convex Surfaces

Author : Herbert Busemann
ISBN : 9780486154992
Genre : Mathematics
File Size : 33.87 MB
Format : PDF, ePub, Docs
Download : 589
Read : 279

This exploration of convex surfaces focuses on extrinsic geometry and applications of the Brunn-Minkowski theory. It also examines intrinsic geometry and the realization of intrinsic metrics. 1958 edition.
Category: Mathematics

Probabilistic Metric Spaces

Author : B. Schweizer
ISBN : 9780486143750
Genre : Mathematics
File Size : 87.76 MB
Format : PDF, ePub
Download : 476
Read : 265

This distinctly nonclassical treatment focuses on developing aspects that differ from the theory of ordinary metric spaces, working directly with probability distribution functions rather than random variables. The two-part treatment begins with an overview that discusses the theory's historical evolution, followed by a development of related mathematical machinery. The presentation defines all needed concepts, states all necessary results, and provides relevant proofs. The second part opens with definitions of probabilistic metric spaces and proceeds to examinations of special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. Throughout, the authors focus on developing aspects that differ from the theory of ordinary metric spaces, rather than simply transferring known metric space results to a more general setting.
Category: Mathematics

The Ricci Flow In Riemannian Geometry

Author : Ben Andrews
ISBN : 9783642162855
Genre : Mathematics
File Size : 84.63 MB
Format : PDF, ePub, Mobi
Download : 921
Read : 996

Focusing on Hamilton's Ricci flow, this volume begins with a detailed discussion of the required aspects of differential geometry. The discussion also includes existence and regularity theory, compactness theorems for Riemannian manifolds, and much more.
Category: Mathematics

Modern Approaches To Discrete Curvature

Author : Laurent Najman
ISBN : 9783319580029
Genre : Mathematics
File Size : 34.20 MB
Format : PDF, Kindle
Download : 427
Read : 517

This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.
Category: Mathematics

In Search Of The Riemann Zeros

Author : Michel Laurent Lapidus
ISBN : 0821842226
Genre : Mathematics
File Size : 55.12 MB
Format : PDF, ePub
Download : 305
Read : 463

Formulated in 1859, the Riemann Hypothesis is the most celebrated and multifaceted open problem in mathematics. In essence, it states that the primes are distributed as harmoniously as possible--or, equivalently, that the Riemann zeros are located on a single vertical line, called the critical line. In this book, the author proposes a new approach to understand and possibly solve the Riemann Hypothesis. His reformulation builds upon earlier (joint) work on complex fractal dimensions and the vibrations of fractal strings, combined with string theory and noncommutative geometry. Accordingly, it relies on the new notion of a fractal membrane or quantized fractal string, along with the modular flow on the associated moduli space of fractal membranes. Conjecturally, under the action of the modular flow, the spacetime geometries become increasingly symmetric and crystal-like, hence, arithmetic. Correspondingly, the zeros of the associated zeta functions eventually condense onto the critical line, towards which they are attracted, thereby explaining why the Riemann Hypothesis must be true. Written with a diverse audience in mind, this unique book is suitable for graduate students, experts and nonexperts alike, with an interest in number theory, analysis, dynamical systems, arithmetic, fractal or noncommutative geometry, and mathematical or theoretical physics.
Category: Mathematics

Needle Decompositions In Riemannian Geometry

Author : Bo’az Klartag
ISBN : 9781470425425
Genre : Curvature
File Size : 76.6 MB
Format : PDF, Docs
Download : 331
Read : 1158

The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Category: Curvature