Search Results for "geometric-analysis-cambridge-studies-in-advanced-mathematics"

Geometric Analysis

Geometric Analysis

  • Author: Peter Li
  • Publisher: Cambridge University Press
  • ISBN: 1107020646
  • Category: Mathematics
  • Page: 406
  • View: 9593
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Basic techniques for researchers interested in the field of geometric analysis.

Introduction To The Geometrical Analysis Of Vector Fields, An: With Applications To Maximum Principles And Lie Groups

Introduction To The Geometrical Analysis Of Vector Fields, An: With Applications To Maximum Principles And Lie Groups

  • Author: Biagi Stefano,Bonfiglioli Andrea
  • Publisher: World Scientific
  • ISBN: 9813276630
  • Category: Mathematics
  • Page: 452
  • View: 3577
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This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis. Once the background material is established, the applications mainly deal with the following meaningful settings:

Featured Reviews in Mathematical Reviews 1997-1999

Featured Reviews in Mathematical Reviews 1997-1999

With Selected Reviews of Classic Books and Papers from 1940-1969

  • Author: Donald G. Babbitt,Jane E. Kister
  • Publisher: American Mathematical Soc.
  • ISBN: 9780821896709
  • Category: Mathematics
  • Page: 541
  • View: 8527
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This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.

Asymptotic Geometric Analysis, Part I

Asymptotic Geometric Analysis, Part I

  • Author: Shiri Artstein-Avidan, Apostolos Giannopoulos, Vitali D. Milman
  • Publisher: American Mathematical Soc.
  • ISBN: 1470421933
  • Category: Functional analysis
  • Page: 451
  • View: 5008
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The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality. The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more.

Geometry, Analysis and Probability

Geometry, Analysis and Probability

In Honor of Jean-Michel Bismut

  • Author: Jean-Benoît Bost,Helmut Hofer,François Labourie,Yves Le Jan,Xiaonan Ma,Weiping Zhang
  • Publisher: Birkhäuser
  • ISBN: 3319496387
  • Category: Mathematics
  • Page: 361
  • View: 6155
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This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.

Geometric Analysis

Geometric Analysis

  • Author: Hubert L. Bray,Greg Galloway,Rafe Mazzeo,Natasa Sesum
  • Publisher: American Mathematical Soc.
  • ISBN: 1470423138
  • Category: Geometric analysis
  • Page: 456
  • View: 4468
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This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace–Beltrami operators.

Real Analysis and Probability

Real Analysis and Probability

  • Author: R. M. Dudley
  • Publisher: Cambridge University Press
  • ISBN: 9780521007542
  • Category: Mathematics
  • Page: 555
  • View: 3240
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This classic graduate textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The comprehensive historical notes have been further amplified for this new edition, and a number of new exercises have been added, together with hints for solution.

Geometric Analysis on the Heisenberg Group and Its Generalizations

Geometric Analysis on the Heisenberg Group and Its Generalizations

  • Author: Ovidiu Calin,Der-chen E. Chang,Peter Charles Greiner
  • Publisher: American Mathematical Soc.
  • ISBN: 9780821843192
  • Category: Mathematics
  • Page: 244
  • View: 7125
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The theory of subRiemannian manifolds is closely related to Hamiltonian mechanics. In this book, the authors examine the properties and applications of subRiemannian manifolds that automatically satisfy the Heisenberg principle, which may be useful in quantum mechanics. In particular, the behavior of geodesics in this setting plays an important role in finding heat kernels and propagators for Schrodinger's equation. One of the novelties of this book is the introduction of techniques from complex Hamiltonian mechanics.

Stone Spaces

Stone Spaces

  • Author: Peter T. Johnstone
  • Publisher: Cambridge University Press
  • ISBN: 9780521337793
  • Category: Mathematics
  • Page: 370
  • View: 8062
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A unified treatment of the corpus of mathematics that has developed out of M. H. Stone's representation theorem for Boolean algebras (1936) which has applications in almost every area of modern mathematics.

Differentialgeometrie, Topologie und Physik

Differentialgeometrie, Topologie und Physik

  • Author: Mikio Nakahara
  • Publisher: Springer-Verlag
  • ISBN: 3662453002
  • Category: Science
  • Page: 597
  • View: 9974
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Differentialgeometrie und Topologie sind wichtige Werkzeuge für die Theoretische Physik. Insbesondere finden sie Anwendung in den Gebieten der Astrophysik, der Teilchen- und Festkörperphysik. Das vorliegende beliebte Buch, das nun erstmals ins Deutsche übersetzt wurde, ist eine ideale Einführung für Masterstudenten und Forscher im Bereich der theoretischen und mathematischen Physik. - Im ersten Kapitel bietet das Buch einen Überblick über die Pfadintegralmethode und Eichtheorien. - Kapitel 2 beschäftigt sich mit den mathematischen Grundlagen von Abbildungen, Vektorräumen und der Topologie. - Die folgenden Kapitel beschäftigen sich mit fortgeschritteneren Konzepten der Geometrie und Topologie und diskutieren auch deren Anwendungen im Bereich der Flüssigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie. - Daran anschließend findet eine Zusammenführung von Geometrie und Topologie statt: es geht um Faserbündel, characteristische Klassen und Indextheoreme (u.a. in Anwendung auf die supersymmetrische Quantenmechanik). - Die letzten beiden Kapitel widmen sich der spannendsten Anwendung von Geometrie und Topologie in der modernen Physik, nämlich den Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer gemetrischen Perspektive. Mikio Nakahara studierte an der Universität Kyoto und am King’s in London Physik sowie klassische und Quantengravitationstheorie. Heute ist er Physikprofessor an der Kinki-Universität in Osaka (Japan), wo er u. a. über topologische Quantencomputer forscht. Diese Buch entstand aus einer Vorlesung, die er während Forschungsaufenthalten an der University of Sussex und an der Helsinki University of Sussex gehalten hat.

Neue Topologische Methoden in der Algebraischen Geometrie

Neue Topologische Methoden in der Algebraischen Geometrie

  • Author: Friedrich Hirzebruch
  • Publisher: Springer-Verlag
  • ISBN: 3662410834
  • Category: Mathematics
  • Page: 165
  • View: 9326
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Geometry of Sets and Measures in Euclidean Spaces

Geometry of Sets and Measures in Euclidean Spaces

Fractals and Rectifiability

  • Author: Pertti Mattila
  • Publisher: Cambridge University Press
  • ISBN: 9780521655958
  • Category: Mathematics
  • Page: 343
  • View: 8152
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This book studies the geometric properties of general sets and measures in euclidean space.

Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis

Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis

  • Author: Gérard Laumon
  • Publisher: Cambridge University Press
  • ISBN: 9780521470605
  • Category: Mathematics
  • Page: 344
  • View: 6704
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This 1995 book introduces the reader to Drinfeld modular varieties, and is pitched at graduate students.

Martingales in Banach Spaces

Martingales in Banach Spaces

  • Author: Gilles Pisier
  • Publisher: Cambridge University Press
  • ISBN: 1107137241
  • Category: Mathematics
  • Page: 560
  • View: 4730
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This book focuses on applications of martingales to the geometry of Banach spaces, and is accessible to graduate students.

Sets of Finite Perimeter and Geometric Variational Problems

Sets of Finite Perimeter and Geometric Variational Problems

An Introduction to Geometric Measure Theory

  • Author: Francesco Maggi
  • Publisher: Cambridge University Press
  • ISBN: 1107021030
  • Category: Mathematics
  • Page: 454
  • View: 5478
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An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers.

The d-bar Neumann Problem and Schrödinger Operators

The d-bar Neumann Problem and Schrödinger Operators

  • Author: Friedrich Haslinger
  • Publisher: Walter de Gruyter GmbH & Co KG
  • ISBN: 3110377837
  • Category: Mathematics
  • Page: 252
  • View: 2948
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The topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations. First we investigate the canonical solution operator to d-bar restricted to Bergman spaces of holomorphic L2 functions in one and several complex variables. These operators are Hankel operators of special type. In the following we consider the general d-bar-complex and derive properties of the complex Laplacian on L2 spaces of bounded pseudoconvex domains and on weighted L2 spaces. The main part is devoted to compactness of the d-bar-Neumann operator. The last part will contain a detailed account of the application of the d-bar-methods to Schrödinger operators, Pauli and Dirac operators and to Witten-Laplacians.

Malliavin Calculus for Lévy Processes with Applications to Finance

Malliavin Calculus for Lévy Processes with Applications to Finance

  • Author: Giulia Di Nunno,Bernt Øksendal,Frank Proske
  • Publisher: Springer Science & Business Media
  • ISBN: 9783540785729
  • Category: Mathematics
  • Page: 418
  • View: 346
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This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.

An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem

An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem

  • Author: Luca Capogna,Donatella Danielli,Scott D. Pauls,Jeremy Tyson
  • Publisher: Springer Science & Business Media
  • ISBN: 3764381337
  • Category: Mathematics
  • Page: 224
  • View: 1059
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This book gives an up-to-date account of progress on Pansu's celebrated problem on the sub-Riemannian isoperimetric profile of the Heisenberg group. It also serves as an introduction to the general field of sub-Riemannian geometric analysis. It develops the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem.