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

## Geometric Analysis

**Author**: Peter Li**Publisher:**Cambridge University Press**ISBN:**1107020646**Category:**Mathematics**Page:**406**View:**8200

Basic techniques for researchers interested in the field of geometric analysis.

## Mathematical Physics, Spectral Theory and Stochastic Analysis

**Author**: Michael Demuth,Werner Kirsch**Publisher:**Springer Science & Business Media**ISBN:**3034805918**Category:**Mathematics**Page:**339**View:**9247

This volume presents self-contained survey articles on modern research areas written by experts in their fields. The topics are located at the interface of spectral theory, theory of partial differential operators, stochastic analysis, and mathematical physics. The articles are accessible to graduate students and researches from other fields of mathematics or physics while also being of value to experts, as they report on the state of the art in the respective fields.

## 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:**4021

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

**Author**: Shiri Artstein-Avidan, Apostolos Giannopoulos, Vitali D. Milman**Publisher:**American Mathematical Soc.**ISBN:**1470421933**Category:**Functional analysis**Page:**451**View:**6670

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

*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:**6527

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

**Author**: Hubert L. Bray,Greg Galloway,Rafe Mazzeo,Natasa Sesum**Publisher:**American Mathematical Soc.**ISBN:**1470423138**Category:**Geometric analysis**Page:**456**View:**4573

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.

## 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:**7561

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

**Author**: Peter T. Johnstone**Publisher:**Cambridge University Press**ISBN:**9780521337793**Category:**Mathematics**Page:**370**View:**5635

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.

## Real Analysis and Probability

**Author**: R. M. Dudley**Publisher:**Cambridge University Press**ISBN:**9780521007542**Category:**Mathematics**Page:**555**View:**955

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.

## Martingales in Banach Spaces

**Author**: Gilles Pisier**Publisher:**Cambridge University Press**ISBN:**1107137241**Category:**Mathematics**Page:**560**View:**609

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

*An Introduction to Geometric Measure Theory*

**Author**: Francesco Maggi**Publisher:**Cambridge University Press**ISBN:**1107021030**Category:**Mathematics**Page:**454**View:**8076

An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers.

## Geometry of Sets and Measures in Euclidean Spaces

*Fractals and Rectifiability*

**Author**: Pertti Mattila**Publisher:**Cambridge University Press**ISBN:**1316583694**Category:**Mathematics**Page:**N.A**View:**2029

Now in paperback, the main theme of this book is the study of geometric properties of general sets and measures in euclidean spaces. Applications of this theory include fractal-type objects such as strange attractors for dynamical systems and those fractals used as models in the sciences. The author provides a firm and unified foundation and develops all the necessary main tools, such as covering theorems, Hausdorff measures and their relations to Riesz capacities and Fourier transforms. The last third of the book is devoted to the Beisovich-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of euclidean space posessing many of the properties of smooth surfaces. These sets have wide application including the higher-dimensional calculus of variations. Their relations to complex analysis and singular integrals are also studied. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.

## 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:**5457

This 1995 book introduces the reader to Drinfeld modular varieties, and is pitched at graduate students.

## Analysis on Lie Groups

*An Introduction*

**Author**: Jacques Faraut**Publisher:**Cambridge University Press**ISBN:**1139471473**Category:**Mathematics**Page:**N.A**View:**2996

The subject of analysis on Lie groups comprises an eclectic group of topics which can be treated from many different perspectives. This self-contained text concentrates on the perspective of analysis, to the topics and methods of non-commutative harmonic analysis, assuming only elementary knowledge of linear algebra and basic differential calculus. The author avoids unessential technical discussions and instead describes in detail many interesting examples, including formulae which have not previously appeared in book form. Topics covered include the Haar measure and invariant integration, spherical harmonics, Fourier analysis and the heat equation, Poisson kernel, the Laplace equation and harmonic functions. Perfect for advanced undergraduates and graduates in geometric analysis, harmonic analysis and representation theory, the tools developed will also be useful for specialists in stochastic calculation and the statisticians. With numerous exercises and worked examples, the text is ideal for a graduate course on analysis on Lie groups.

## Fourier Analysis and Hausdorff Dimension

**Author**: Pertti Mattila**Publisher:**Cambridge University Press**ISBN:**1316352528**Category:**Mathematics**Page:**N.A**View:**6241

During the past two decades there has been active interplay between geometric measure theory and Fourier analysis. This book describes part of that development, concentrating on the relationship between the Fourier transform and Hausdorff dimension. The main topics concern applications of the Fourier transform to geometric problems involving Hausdorff dimension, such as Marstrand type projection theorems and Falconer's distance set problem, and the role of Hausdorff dimension in modern Fourier analysis, especially in Kakeya methods and Fourier restriction phenomena. The discussion includes both classical results and recent developments in the area. The author emphasises partial results of important open problems, for example, Falconer's distance set conjecture, the Kakeya conjecture and the Fourier restriction conjecture. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.

## Geometry, Analysis and Topology of Discrete Groups

**Author**: Lizhen Ji**Publisher:**International Pressof Boston Incorporated**ISBN:**9781571461261**Category:**Mathematics**Page:**468**View:**6935

Discrete subgroups of Lie groups are foundational objects in modern mathematics and occur naturally in different subjects. This new volume presents 15 papers treating discrete groups as they occur in areas such as algebra, analysis, geometry, number theory, and topology. Most of the papers are surveys, and the volume is intended to help graduate students and researchers better understand the structures and applications of discrete subgroups of Lie groups and locally symmetric spaces.

## A Primer of Nonlinear Analysis

**Author**: Antonio Ambrosetti,Giovanni Prodi**Publisher:**Cambridge University Press**ISBN:**9780521485739**Category:**Mathematics**Page:**171**View:**8325

This is an elementary and self-contained introduction to nonlinear functional analysis and its applications, especially in bifurcation theory.

## Mathematisches Denken

*Vom Vergnügen am Umgang mit Zahlen*

**Author**: T.W. Körner**Publisher:**Springer-Verlag**ISBN:**3034850018**Category:**Science**Page:**719**View:**3064

Dieses Buch wendet sich zuallererst an intelligente Schüler ab 14 Jahren sowie an Studienanfänger, die sich für Mathematik interessieren und etwas mehr als die Anfangsgründe dieser Wissenschaft kennenlernen möchten. Es gibt inzwischen mehrere Bücher, die eine ähnliche Zielstellung verfolgen. Besonders gern erinnere ich mich an das Werk Vom Einmaleins zum Integral von Colerus, das ich in meiner Kindheit las. Es beginnt mit der folgenden entschiedenen Feststellung: Die Mathematik ist eine Mausefalle. Wer einmal in dieser Falle gefangen sitzt, findet selten den Ausgang, der zurück in seinen vormathematischen Seelenzustand leitet. ([49], S. 7) Einige dieser Bücher sind im Anhang zusammengestellt und kommen tiert. Tatsächlich ist das Unternehmen aber so lohnenswert und die Anzahl der schon vorhandenen Bücher doch so begrenzt, daß ich mich nicht scheue, ihnen ein weiteres hinzuzufügen. An zahlreichen amerikanischen Universitäten gibt es Vorlesungen, die gemeinhin oder auch offiziell als ,,Mathematik für Schöngeister'' firmieren. Dieser Kategorie ist das vorliegende Buch nicht zuzuordnen. Statt dessen soll es sich um eine ,,Mathematik für Mathematiker'' handeln, für Mathema tiker freilich, die noch sehr wenig von der Mathematik verstehen. Weshalb aber sollte nicht der eine oder andere von ihnen eines Tages den Autor dieses 1 Buches durch seine Vorlesungen in Staunen versetzen? Ich hoffe, daß auch meine Mathematikerkollegen Freude an dem Werk haben werden, und ich würde mir wünschen, daß auch andere Leser, bei denen die Wertschätzung für die Mathematik stärker als die Furcht vor ihr ist, Gefallen an ihm finden mögen.