Pure Metric Geometry
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Pure Metric Geometry
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Author : Anton Petrunin
language : en
Publisher: Springer Nature
Release Date : 2023-12-23
Pure Metric Geometry written by Anton Petrunin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-23 with Mathematics categories.
This book serves as an introductory asset for learning metric geometry by delivering an in-depth examination of key constructions and providing an analysis of universal spaces, injective spaces, the Gromov-Hausdorff convergence, and ultralimits. This book illustrates basic examples of domestic affairs of metric spaces, this includes Alexandrov geometry, geometric group theory, metric-measure spaces and optimal transport. Researchers in metric geometry will find this book appealing and helpful, in addition to graduate students in mathematics, and advanced undergraduate students in need of an introduction to metric geometry. Any previous knowledge of classical geometry, differential geometry, topology, and real analysis will be useful in understanding the presented topics.
A Course In Metric Geometry
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Author : Dmitri Burago
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
A Course In Metric Geometry written by Dmitri Burago and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
"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).
Encyclopedia Of Distances
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Author : Michel Marie Deza
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-28
Encyclopedia Of Distances written by Michel Marie Deza and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-28 with Mathematics categories.
Distance metrics and distances have become an essential tool in many areas of pure and applied Mathematics, and this encyclopedia is the first one to treat the subject in full. The book appears just as research intensifies into metric spaces and especially, distance design for applications. These distances are particularly crucial, for example, in computational biology, image analysis, speech recognition, and information retrieval. Here, an assessment of the practical questions arising during selection of a "good'' distance function has been left aside in favor of a comprehensive listing of the main available distances, a useful tool for the distance design community. This reader-friendly reference offers both independent introductions and definitions, while at the same time making cross-referencing easy through hyperlink-like boldfaced references to original definitions. This high-quality publication is a mix of reference resource and coffee-table book.
Groupoid Metrization Theory
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Author : Dorina Mitrea
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-15
Groupoid Metrization Theory written by Dorina Mitrea and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-15 with Mathematics categories.
The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry. The presentation is self-contained with complete, detailed proofs, and a large number of examples and counterexamples are provided. Unique features of Metrization Theory for Groupoids: With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis include: * treatment of metrization from a wide, interdisciplinary perspective, with accompanying applications ranging across diverse fields; * coverage of topics applicable to a variety of scientific areas within pure mathematics; * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. * coverage of topics applicable to a variety of scientific areas within pure mathematics; * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties.
Elementary Synthetic Geometry
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Author : George Bruce Halsted
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2015-11-06
Elementary Synthetic Geometry written by George Bruce Halsted and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-06 with categories.
From the PREFACE TO THE THIRD EDITION. Researches in the non-Euclidean geometries of Bolyai-Lobachévski and Riemann, while renewing the traditional admiration for Euclid, yet emphasize the advantages of a comparative study of pure spherics and plane geometry before similar figures. Putting pure spherics as Book II is thus a beginning toward comparative geometry. Again, the non-Euclidean geometry has given the key to the artificiality in Euclid's order of propositions. But it is approaching metric geometry from pure projective geometry which decides in favor of symmetry as a guiding principle. George Bruce Halsted. 2407 Guadalupe Street, Austin, Texas.
Recent Topics In Differential And Analytic Geometry
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Author : T. Ochiai
language : en
Publisher: Academic Press
Release Date : 2014-07-14
Recent Topics In Differential And Analytic Geometry written by T. Ochiai and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains. Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters consider the most recognized non-standard examples of compact homogeneous Einstein manifolds constructed via Riemannian submersions. This book discusses as well the natural compactification of the moduli space of polarized Einstein–Kähler orbitfold with a given Hilbert polynomials. The final chapter deals with solving a degenerate Monge–Ampère equation by constructing a family of Einstein–Kähler metrics on the smooth part of minimal varieties of general kind. This book is a valuable resource for graduate students and pure mathematicians.
Metric Spaces Convexity And Non Positive Curvature
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Author : Athanase Papadopoulos
language : en
Publisher: Erich Schmidt Verlag GmbH & Co. KG
Release Date : 2014
Metric Spaces Convexity And Non Positive Curvature written by Athanase Papadopoulos and has been published by Erich Schmidt Verlag GmbH & Co. KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Convex domains categories.
This book is about metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function satisfies a convexity condition. The book also contains a systematic introduction to metric geometry, as well as a detailed presentation of some facets of convexity theory that are useful in the study of nonpositive curvature. The concepts and the techniques are illustrated by many examples, in particular from hyperbolic geometry, Hilbert geometry and Teichmuller theory. For the second edition, some corrections and a few additions have been made, and the bibliography has been updated.
K Hler Metric And Moduli Spaces
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Author : T. Ochiai
language : en
Publisher: Academic Press
Release Date : 2013-10-22
K Hler Metric And Moduli Spaces written by T. Ochiai and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Mathematics categories.
Kähler Metric and Moduli Spaces, Volume 18-II covers survey notes from the expository lectures given during the seminars in the academic year of 1987 for graduate students and mature mathematicians who were not experts on the topics considered during the sessions about partial differential equations. The book discusses basic facts on Einstein metrics in complex geometry; Einstein-Kähler metrics with positive or non-positive Ricci curvature; Yang-Mills connections; and Einstein-Hermitian metrics. The text then describes the tangent sheaves of minimal varieties; Ricci-Flat Kähler metrics on affine algebraic manifolds; and degenerations of Kähler-Einstein. The moduli of Einstein metrics on a K3 surface and degeneration of Type I and the uniformization of complex surfaces are also considered. Mathematicians and graduate students taking differential and analytic geometry will find the book useful.
Metric Spaces Of Non Positive Curvature
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Author : Martin R. Bridson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Metric Spaces Of Non Positive Curvature written by Martin R. Bridson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. The theory of these objects is developed in a manner accessible to anyone familiar with the rudiments of topology and group theory: non-trivial theorems are proved by concatenating elementary geometric arguments, and many examples are given. Part I provides an introduction to the geometry of geodesic spaces, while Part II develops the basic theory of spaces with upper curvature bounds. More specialized topics, such as complexes of groups, are covered in Part III.
Projective Geometry And Projective Metrics
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Author : Herbert Busemann
language : en
Publisher:
Release Date : 1953
Projective Geometry And Projective Metrics written by Herbert Busemann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953 with Elliptic space categories.
The present book differs widely in content, methods, and point of view from traditional presentations of the subject. Herein more space is devoted to the discussion of the basic concepts of distance, motion, area and perpendicularity. In fact, the non-Euclidean geometries are reached via general metric spaces and the Hilbert problem of finding those geometries in which straight lines are the shortest connections. Of course, the general problem is only formulated here; but this leads naturally to the consideration of geometries other than the Euclidean and two non-Euclidean ones, and thus to the modern view in which the three classical geometries are very special, and closely related, cases of general geometric structures. The overall aim is to counteract the impression of geometry as an isolated and static subject, and to present its methods and essential content as part of modern mathematics.