Foundations of Hyperbolic Manifolds


Author: John Ratcliffe
Publisher: Springer Science & Business Media
ISBN: 1475740131
Category: Mathematics
Page: 750
View: 3015
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This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem.

Foundations of Hyperbolic Manifolds


Author: John G. Ratcliffe
Publisher: Springer Science & Business Media
ISBN: 9780387942490
Category: Mathematics
Page: 747
View: 6595
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Fundamentals of Hyperbolic Manifolds

Selected Expositions
Author: R. D. Canary,A. Marden,D. B. A. Epstein
Publisher: Cambridge University Press
ISBN: 0521615585
Category: Mathematics
Page: 335
View: 5199
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Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.

Hyperbolic Manifolds


Author: Albert Marden
Publisher: Cambridge University Press
ISBN: 1107116740
Category: Mathematics
Page: 550
View: 2507
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Second edition of Outer circles, which has changed title to: Hyperbolic manifolds.

The Coxeter Legacy

Reflections and Projections
Author: Harold Scott Macdonald Coxeter,Chandler Davis,Erich W. Ellers
Publisher: American Mathematical Soc.
ISBN: 9780821887608
Category: Mathematics
Page: 320
View: 7556
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This collection of essays on the legacy of mathematican Donald Coxeter is a mixture of surveys, updates, history, storytelling and personal memories covering both applied and abstract maths. Subjects include: polytopes, Coxeter groups, equivelar polyhedra, Ceva's theorum, and Coxeter and the artists.

Maß und Kategorie


Author: J.C. Oxtoby
Publisher: Springer-Verlag
ISBN: 364296074X
Category: Mathematics
Page: 112
View: 8137
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Dieses Buch behandelt hauptsächlich zwei Themenkreise: Der Bairesche Kategorie-Satz als Hilfsmittel für Existenzbeweise sowie Die "Dualität" zwischen Maß und Kategorie. Die Kategorie-Methode wird durch viele typische Anwendungen erläutert; die Analogie, die zwischen Maß und Kategorie besteht, wird nach den verschiedensten Richtungen hin genauer untersucht. Hierzu findet der Leser eine kurze Einführung in die Grundlagen der metrischen Topologie; außerdem werden grundlegende Eigenschaften des Lebesgue schen Maßes hergeleitet. Es zeigt sich, daß die Lebesguesche Integrationstheorie für unsere Zwecke nicht erforderlich ist, sondern daß das Riemannsche Integral ausreicht. Weiter werden einige Begriffe aus der allgemeinen Maßtheorie und Topologie eingeführt; dies geschieht jedoch nicht nur der größeren Allgemeinheit wegen. Es erübrigt sich fast zu erwähnen, daß sich die Bezeichnung "Kategorie" stets auf "Bairesche Kategorie" be zieht; sie hat nichts zu tun mit dem in der homologischen Algebra verwendeten Begriff der Kategorie. Beim Leser werden lediglich grundlegende Kenntnisse aus der Analysis und eine gewisse Vertrautheit mit der Mengenlehre vorausgesetzt. Für die hier untersuchten Probleme bietet sich in natürlicher Weise die mengentheoretische Formulierung an. Das vorlie gende Buch ist als Einführung in dieses Gebiet der Analysis gedacht. Man könnte es als Ergänzung zur üblichen Grundvorlesung über reelle Analysis, als Grundlage für ein Se minar oder auch zum selbständigen Studium verwenden. Bei diesem Buch handelt es sich vorwiegend um eine zusammenfassende Darstellung; jedoch finden sich in ihm auch einige Verfeinerungen bekannter Resultate, namentlich Satz 15.6 und Aussage 20.4. Das Literaturverzeichnis erhebt keinen Anspruch auf Vollständigkeit. Häufig werden Werke zitiert, die weitere Literaturangaben enthalten.

Vorlesungen über die Theorie der algebraischen Zahlen


Author: Erich Hecke
Publisher: University of Pennsylvania Press
ISBN: 9780821821435
Category: Mathematics
Page: 274
View: 3307
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This title has been described as An elegant and comprehensive account of the modern theory of algebraic numbers - Bulletin of the AMS.

Lehrbuch der Topologie


Author: Herbert Seifert,William Threlfall
Publisher: University of Pennsylvania Press
ISBN: 9780821835951
Category: Mathematics
Page: 353
View: 4355
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The 1930s were important years in the development of modern topology, pushed forward by the appearance of a few pivotal books, of which this is one. The focus is on combinatorial and algebraic topology, with as much point-set topology as needed for the main topics. One sees from the modern point of view that the authors are working in a category of spaces that includes locally finite simplicial complexes. (Their definition of manifold is more properly known today as a ""triangulizable homology manifold"".)Amazingly, they manage to accomplish a lot without the convenient tools of homological algebra, such as exact sequences and commutative diagrams, that were developed later. The main topics covered are: simplicial homology (coefficients in $\mathbb{Z}$ or $\mathbb{Z}_2$), local homology, surface topology, the fundamental group and covering spaces, three-manifolds, Poincare duality, and the Lefschetz fixed point theorem. Few prerequisites are necessary. A final section reviews the lemmas and theorems from group theory that are needed in the text. As stated in the introduction to the important book by Alexandroff and Hopf (which appeared a year after ""Seifert and Threlfall""): 'Its lively and instructive presentation makes this book particularly suitable as an introduction or as a textbook.'

Partielle Differentialgleichungen

Eine Einführung
Author: Walter A. Strauss
Publisher: Springer-Verlag
ISBN: 366312486X
Category: Mathematics
Page: 458
View: 2071
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Dieses Buch ist eine umfassende Einführung in die klassischen Lösungsmethoden partieller Differentialgleichungen. Es wendet sich an Leser mit Kenntnissen aus einem viersemestrigen Grundstudium der Mathematik (und Physik) und legt seinen Schwerpunkt auf die explizite Darstellung der Lösungen. Es ist deshalb besonders auch für Anwender (Physiker, Ingenieure) sowie für Nichtspezialisten, die die Methoden der mathematischen Physik kennenlernen wollen, interessant. Durch die große Anzahl von Beispielen und Übungsaufgaben eignet es sich gut zum Gebrauch neben Vorlesungen sowie zum Selbststudium.

Analysis und mathematische Physik


Author: Hans Triebel
Publisher: Springer-Verlag
ISBN: 3034852657
Category: Juvenile Nonfiction
Page: 451
View: 7720
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Real and Abstract Analysis

A modern treatment of the theory of functions of a real variable
Author: Edwin Hewitt,Karl Stromberg
Publisher: Springer-Verlag
ISBN: 3662297949
Category: Mathematics
Page: 476
View: 8274
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Dirichlet Forms and Analysis on Wiener Space


Author: Nicolas Bouleau,Francis Hirsch
Publisher: Walter de Gruyter
ISBN: 311085838X
Category: Mathematics
Page: 335
View: 5522
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The subject of this book is analysis on Wiener space by means of Dirichlet forms and Malliavin calculus. There are already several literature on this topic, but this book has some different viewpoints. First the authors review the theory of Dirichlet forms, but they observe only functional analytic, potential theoretical and algebraic properties. They do not mention the relation with Markov processes or stochastic calculus as discussed in usual books (e.g. Fukushima’s book). Even on analytic properties, instead of mentioning the Beuring-Deny formula, they discuss “carré du champ” operators introduced by Meyer and Bakry very carefully. Although they discuss when this “carré du champ” operator exists in general situation, the conditions they gave are rather hard to verify, and so they verify them in the case of Ornstein-Uhlenbeck operator in Wiener space later. (It should be noticed that one can easily show the existence of “carré du champ” operator in this case by using Shigekawa’s H-derivative.) In the part on Malliavin calculus, the authors mainly discuss the absolute continuity of the probability law of Wiener functionals. The Dirichlet form corresponds to the first derivative only, and so it is not easy to consider higher order derivatives in this framework. This is the reason why they discuss only the first step of Malliavin calculus. On the other hand, they succeeded to deal with some delicate problems (the absolute continuity of the probability law of the solution to stochastic differential equations with Lipschitz continuous coefficients, the domain of stochastic integrals (Itô-Ramer-Skorokhod integrals), etc.). This book focuses on the abstract structure of Dirichlet forms and Malliavin calculus rather than their applications. However, the authors give a lot of exercises and references and they may help the reader to study other topics which are not discussed in this book. Zentralblatt Math, Reviewer: S.Kusuoka (Hongo)

Manifolds and Modular Forms


Author: Friedrich Hirzebruch
Publisher: Springer-Verlag
ISBN: 3663140458
Category: Mathematics
Page: 212
View: 2510
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Lineare Algebra


Author: Werner Greub
Publisher: Springer-Verlag
ISBN: 3642663850
Category: Mathematics
Page: 222
View: 9149
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On volumes of some hyperbolic 3-manifolds


Author: Andrei Vesnin
Publisher: N.A
ISBN: N.A
Category: Three-manifolds (Topology)
Page: 132
View: 2206
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Kategorien und Funktoren


Author: Bodo Pareigis
Publisher: N.A
ISBN: N.A
Category: Categories (Mathematics)
Page: 192
View: 5262
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Journal of the Korean Mathematical Society


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 445
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Four-manifolds, geometries and knots


Author: Jonathan Arthur Hillman,University of Warwick. Mathematics Institute
Publisher: N.A
ISBN: N.A
Category: Four-manifolds (Topology)
Page: 379
View: 8785
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Pacific Journal of Mathematics


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 1590
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Höhere Mathematik

für Ingenieure, Physiker und Mathematiker
Author: Norbert Herrmann
Publisher: Oldenbourg Verlag
ISBN: 9783486274981
Category:
Page: 507
View: 9407
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Das Lehrbuch deckt die wichtigsten Themen ab, mit denen sich Ingenieure und Physiker nach den Einführungsvorlesungen aus der Analysis und der linearen Algebra beschäftigen. Der Schwerpunkt der Darstellung liegt auf den für Ingenieure und Physiker wichtigen numerischen Verfahren, die auch für an Anwendungen interessierte Mathematiker von elementarer Bedeutung sind. Der Autor veranschaulicht anhand einer Vielzahl von Beispielen und in einer leicht verständlichen Sprache die Inhalte. Ausgehend von den Grundlagen nähert er sich schrittweise komplexen Themen an und skizziert Beweise, sofern sie für das Verständnis hilfreich sind. Das Buch ist damit hervorragend zur Prüfungsvorbereitung geeignet!