Riemannian Metrics of Constant Mass and Moduli Spaces of Conformal Structures

Riemannian Metrics of Constant Mass and Moduli Spaces of Conformal Structures
Author: Lutz Habermann
Publisher: Springer
Total Pages: 123
Release: 2007-05-06
Genre: Mathematics
ISBN: 3540444432

This monograph deals with recent questions of conformal geometry. It provides in detail an approach to studying moduli spaces of conformal structures, using a new canonical metric for conformal structures. This book is accessible to readers with basic knowledge in differential geometry and global analysis. It addresses graduates and researchers.

Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry

Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry
Author: Ye-lin Ou
Publisher: World Scientific
Total Pages: 541
Release: 2020-04-04
Genre: Mathematics
ISBN: 9811212392

The book aims to present a comprehensive survey on biharmonic submanifolds and maps from the viewpoint of Riemannian geometry. It provides some basic knowledge and tools used in the study of the subject as well as an overall picture of the development of the subject with most up-to-date important results.Biharmonic submanifolds are submanifolds whose isometric immersions are biharmonic maps, thus biharmonic submanifolds include minimal submanifolds as a subclass. Biharmonic submanifolds also appeared in the study of finite type submanifolds in Euclidean spaces.Biharmonic maps are maps between Riemannian manifolds that are critical points of the bienergy. They are generalizations of harmonic maps and biharmonic functions which have many important applications and interesting links to many areas of mathematics and theoretical physics.Since 2000, biharmonic submanifolds and maps have become a vibrant research field with a growing number of researchers around the world, with many interesting results have been obtained.This book containing basic knowledge, tools for some fundamental problems and a comprehensive survey on the study of biharmonic submanifolds and maps will be greatly beneficial for graduate students and beginning researchers who want to study the subject, as well as researchers who have already been working in the field.

Conformal Geometry of Surfaces in S4 and Quaternions

Conformal Geometry of Surfaces in S4 and Quaternions
Author: Francis E. Burstall
Publisher: Springer
Total Pages: 98
Release: 2004-10-19
Genre: Mathematics
ISBN: 3540453016

The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Bäcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.

Perspectives In Scalar Curvature (In 2 Volumes)

Perspectives In Scalar Curvature (In 2 Volumes)
Author: Mikhail L Gromov
Publisher: World Scientific
Total Pages: 1635
Release: 2022-12-19
Genre: Mathematics
ISBN: 9811249377

Volume I contains a long article by Misha Gromov based on his many years of involvement in this subject. It came from lectures delivered in Spring 2019 at IHES. There is some background given. Many topics in the field are presented, and many open problems are discussed. One intriguing point here is the crucial role played by two seemingly unrelated analytic means: index theory of Dirac operators and geometric measure theory.Very recently there have been some real breakthroughs in the field. Volume I has several survey articles written by people who were responsible for these results.For Volume II, many people in areas of mathematics and physics, whose work is somehow related to scalar curvature, were asked to write about this in any way they pleased. This gives rise to a wonderful collection of articles, some with very broad and historical views, others which discussed specific fascinating subjects.These two books give a rich and powerful view of one of geometry's very appealing sides.

Theory of K-Loops

Theory of K-Loops
Author: Hubert Kiechle
Publisher: Springer
Total Pages: 200
Release: 2004-10-12
Genre: Mathematics
ISBN: 3540458174

The book contains the first systematic exposition of the current known theory of K-loops, as well as some new material. In particular, big classes of examples are constructed. The theory for sharply 2-transitive groups is generalized to the theory of Frobenius groups with many involutions. A detailed discussion of the relativistic velocity addition based on the author's construction of K-loops from classical groups is also included. The first chapters of the book can be used as a text, the later chapters are research notes, and only partially suitable for the classroom. The style is concise, but complete proofs are given. The prerequisites are a basic knowledge of algebra such as groups, fields, and vector spaces with forms.

Osserman Manifolds in Semi-Riemannian Geometry

Osserman Manifolds in Semi-Riemannian Geometry
Author: Eduardo Garcia-Rio
Publisher: Springer Science & Business Media
Total Pages: 184
Release: 2002-02-25
Genre: Mathematics
ISBN: 9783540431442

The subject of this book is Osserman semi-Riemannian manifolds, and in particular, the Osserman conjecture in semi-Riemannian geometry. The treatment is pitched at the intermediate graduate level and requires some intermediate knowledge of differential geometry. The notation is mostly coordinate-free and the terminology is that of modern differential geometry. Known results toward the complete proof of Riemannian Osserman conjecture are given and the Osserman conjecture in Lorentzian geometry is proved completely. Counterexamples to the Osserman conjuncture in generic semi-Riemannian signature are provided and properties of semi-Riemannian Osserman manifolds are investigated.

Monotone Random Systems Theory and Applications

Monotone Random Systems Theory and Applications
Author: Igor Chueshov
Publisher: Springer
Total Pages: 239
Release: 2004-10-11
Genre: Mathematics
ISBN: 3540458158

The aim of this book is to present a recently developed approach suitable for investigating a variety of qualitative aspects of order-preserving random dynamical systems and to give the background for further development of the theory. The main objects considered are equilibria and attractors. The effectiveness of this approach is demonstrated by analysing the long-time behaviour of some classes of random and stochastic ordinary differential equations which arise in many applications.

Pointwise Convergence of Fourier Series

Pointwise Convergence of Fourier Series
Author: Juan Arias de Reyna
Publisher: Springer
Total Pages: 180
Release: 2004-10-13
Genre: Mathematics
ISBN: 3540458220

This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.

Asymptotic Behavior of Dynamical and Control Systems under Pertubation and Discretization

Asymptotic Behavior of Dynamical and Control Systems under Pertubation and Discretization
Author: Lars Grüne
Publisher: Springer
Total Pages: 241
Release: 2004-10-19
Genre: Mathematics
ISBN: 3540367845

This book provides an approach to the study of perturbation and discretization effects on the long-time behavior of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors, asumptotically controllable sets and their respective domains of attractions and reachable sets. Combining robust stability concepts from nonlinear control theory, techniques from optimal control and differential games and methods from nonsmooth analysis, both qualitative and quantitative results are obtained and new algorithms are developed, analyzed and illustrated by examples.

Asymptotic Behavior of Dynamical and Control Systems Under Perturbation and Discretization

Asymptotic Behavior of Dynamical and Control Systems Under Perturbation and Discretization
Author: Lars Grüne
Publisher:
Total Pages: 248
Release: 2002
Genre: Asymptotes
ISBN: 9780540433919

This text provides an approach to the study of perturbation and discretization effects on the long-time behaviour of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors and asumptotically controllable sets.