Coulomb Frames In The Normal Bundle Of Surfaces In Euclidean Spaces

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Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces

Steffen Fröhlich
Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces Book PDF

Author : Steffen Fröhlich
Publisher : Springer
Page : 128 pages
File Size : 42,9 Mb
Release : 2012-06-30
Category : Mathematics
ISBN : 9783642298462

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Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces by Steffen Fröhlich Pdf

This book is intended for advanced students and young researchers interested in the analysis of partial differential equations and differential geometry. It discusses elementary concepts of surface geometry in higher-dimensional Euclidean spaces, in particular the differential equations of Gauss-Weingarten together with various integrability conditions and corresponding surface curvatures. It includes a chapter on curvature estimates for such surfaces, and, using results from potential theory and harmonic analysis, it addresses geometric and analytic methods to establish the existence and regularity of Coulomb frames in their normal bundles, which arise as critical points for a functional of total torsion.

Differential Forms in Algebraic Topology

Raoul Bott,Loring W. Tu
Differential Forms in Algebraic Topology Book PDF

Author : Raoul Bott,Loring W. Tu
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 50,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475739510

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Differential Forms in Algebraic Topology by Raoul Bott,Loring W. Tu Pdf

Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.

The Geometry of Heisenberg Groups

Ernst Binz,Sonja Pods
The Geometry of Heisenberg Groups Book PDF

Author : Ernst Binz,Sonja Pods
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 42,5 Mb
Release : 2008
Category : Heisenberg uncertainty principle
ISBN : 9780821844953

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The Geometry of Heisenberg Groups by Ernst Binz,Sonja Pods Pdf

"The three-dimensional Heisenberg group, being a quite simple non-commutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered." "This book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics."--BOOK JACKET.

Handbook of Global Analysis

Demeter Krupka,David Saunders
Handbook of Global Analysis Book PDF

Author : Demeter Krupka,David Saunders
Publisher : Elsevier
Page : 1243 pages
File Size : 47,9 Mb
Release : 2011-08-11
Category : Mathematics
ISBN : 9780080556734

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Handbook of Global Analysis by Demeter Krupka,David Saunders Pdf

This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents

Strings and Geometry

Clay Mathematics Institute. Summer School,Isaac Newton Institute for Mathematical Sciences
Strings and Geometry Book PDF

Author : Clay Mathematics Institute. Summer School,Isaac Newton Institute for Mathematical Sciences
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 46,5 Mb
Release : 2004
Category : Mathematics
ISBN : 082183715X

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Strings and Geometry by Clay Mathematics Institute. Summer School,Isaac Newton Institute for Mathematical Sciences Pdf

Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.

Eigenfunctions of the Laplacian on a Riemannian Manifold

Steve Zelditch
Eigenfunctions of the Laplacian on a Riemannian Manifold Book PDF

Author : Steve Zelditch
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 47,8 Mb
Release : 2017-12-12
Category : Eigenfunctions
ISBN : 9781470410377

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Eigenfunctions of the Laplacian on a Riemannian Manifold by Steve Zelditch Pdf

Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.

Geometric Analysis

Ailana Fraser,André Neves,Peter M. Topping,Paul C. Yang
Geometric Analysis Book PDF

Author : Ailana Fraser,André Neves,Peter M. Topping,Paul C. Yang
Publisher : Springer Nature
Page : 146 pages
File Size : 45,6 Mb
Release : 2020-08-20
Category : Mathematics
ISBN : 9783030537258

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Geometric Analysis by Ailana Fraser,André Neves,Peter M. Topping,Paul C. Yang Pdf

This book covers recent advances in several important areas of geometric analysis including extremal eigenvalue problems, mini-max methods in minimal surfaces, CR geometry in dimension three, and the Ricci flow and Ricci limit spaces. An output of the CIME Summer School "Geometric Analysis" held in Cetraro in 2018, it offers a collection of lecture notes prepared by Ailana Fraser (UBC), André Neves (Chicago), Peter M. Topping (Warwick), and Paul C. Yang (Princeton). These notes will be a valuable asset for researchers and advanced graduate students in geometric analysis.

Microlocal Methods in Mathematical Physics and Global Analysis

Daniel Grieser,Stefan Teufel,Andras Vasy
Microlocal Methods in Mathematical Physics and Global Analysis Book PDF

Author : Daniel Grieser,Stefan Teufel,Andras Vasy
Publisher : Springer Science & Business Media
Page : 148 pages
File Size : 55,7 Mb
Release : 2012-12-13
Category : Mathematics
ISBN : 9783034804660

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Microlocal Methods in Mathematical Physics and Global Analysis by Daniel Grieser,Stefan Teufel,Andras Vasy Pdf

Microlocal analysis is a field of mathematics that was invented in the mid-20th century for the detailed investigation of problems from partial differential equations, which incorporated and made rigorous many ideas that originated in physics. Since then it has grown to a powerful machine which is used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. In this book extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held at the University of Tübingen from the 14th to the 18th of June 2011, are collected.​

Lectures on Choquet's Theorem

Robert Ralph Phelps
Lectures on Choquet s Theorem Book PDF

Author : Robert Ralph Phelps
Publisher : Unknown
Page : 144 pages
File Size : 47,5 Mb
Release : 1966
Category : Choquet theory
ISBN : UOM:39015001316713

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Lectures on Choquet's Theorem by Robert Ralph Phelps Pdf

Appearing for the first time in book form are the main results centered about Choquet's integral representation theorem-an important recent chapter in functional analysis. This theorem has applications to analysis, probability, potential theory, and functional analysis; it will doubtless have further applications as it becomes better known. This readable book presupposes a knowledge of integration theory and elementary functional analysis, including the Krein-Milman theorem and the Riesz representation theorem. --Back cover.

Methods of Information Geometry

Shun-ichi Amari,Hiroshi Nagaoka
Methods of Information Geometry Book PDF

Author : Shun-ichi Amari,Hiroshi Nagaoka
Publisher : American Mathematical Soc.
Page : 220 pages
File Size : 40,6 Mb
Release : 2000
Category : Computers
ISBN : 0821843028

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Methods of Information Geometry by Shun-ichi Amari,Hiroshi Nagaoka Pdf

Information geometry provides the mathematical sciences with a fresh framework of analysis. This book presents a comprehensive introduction to the mathematical foundation of information geometry. It provides an overview of many areas of applications, such as statistics, linear systems, information theory, quantum mechanics, and convex analysis.

Modern General Relativity

M. W. Guidry,Mike Guidry
Modern General Relativity Book PDF

Author : M. W. Guidry,Mike Guidry
Publisher : Cambridge University Press
Page : 625 pages
File Size : 51,6 Mb
Release : 2019-01-03
Category : Science
ISBN : 9781107197893

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Modern General Relativity by M. W. Guidry,Mike Guidry Pdf

Introduces the physics of general relativity in relation to modern topics such as gamma-ray bursts, black holes, and gravitational waves.

Problems and Solutions in Differential Geometry, Lie Series, Differential Forms, Relativity and Applications

Willi-Hans Steeb
Problems and Solutions in Differential Geometry Lie Series Differential Forms Relativity and Applications Book PDF

Author : Willi-Hans Steeb
Publisher : World Scientific Publishing Company
Page : 296 pages
File Size : 45,9 Mb
Release : 2017-10-20
Category : Mathematics
ISBN : 9789813230842

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Problems and Solutions in Differential Geometry, Lie Series, Differential Forms, Relativity and Applications by Willi-Hans Steeb Pdf

This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer–Cartan form, and the Lie derivative are covered. Readers will find useful applications to special and general relativity, Yang–Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry. Request Inspection Copy

Dynamical Systems IV

V.I. Arnol'd,S.P. Novikov
Dynamical Systems IV Book PDF

Author : V.I. Arnol'd,S.P. Novikov
Publisher : Springer Science & Business Media
Page : 291 pages
File Size : 52,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662067932

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Dynamical Systems IV by V.I. Arnol'd,S.P. Novikov Pdf

This book takes a snapshot of the mathematical foundations of classical and quantum mechanics from a contemporary mathematical viewpoint. It covers a number of important recent developments in dynamical systems and mathematical physics and places them in the framework of the more classical approaches; the presentation is enhanced by many illustrative examples concerning topics which have been of especial interest to workers in the field, and by sketches of the proofs of the major results. The comprehensive bibliographies are designed to permit the interested reader to retrace the major stages in the development of the field if he wishes. Not so much a detailed textbook for plodding students, this volume, like the others in the series, is intended to lead researchers in other fields and advanced students quickly to an understanding of the 'state of the art' in this area of mathematics. As such it will serve both as a basic reference work on important areas of mathematical physics as they stand today, and as a good starting point for further, more detailed study for people new to this field.

Trends in Complex Analysis, Differential Geometry, and Mathematical Physics

Stancho Dimiev,Kouei Sekigawa
Trends in Complex Analysis Differential Geometry and Mathematical Physics Book PDF

Author : Stancho Dimiev,Kouei Sekigawa
Publisher : World Scientific
Page : 248 pages
File Size : 40,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812384522

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Trends in Complex Analysis, Differential Geometry, and Mathematical Physics by Stancho Dimiev,Kouei Sekigawa Pdf

The Sixth International Workshop on Complex Structures and Vector Fields was a continuation of the previous five workshops (1992, 1994, 1996, 1998, 2000) on similar research projects. This series of workshops aims at higher achievements in studies of new research subjects. The present volume will meet with the satisfaction of many readers.

Geometric Optics on Phase Space

Kurt Bernardo Wolf
Geometric Optics on Phase Space Book PDF

Author : Kurt Bernardo Wolf
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 43,5 Mb
Release : 2004-07-21
Category : Science
ISBN : 3540220399

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Geometric Optics on Phase Space by Kurt Bernardo Wolf Pdf

Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geometric or wave) have an even richer symmetry structure than mechanical ones (classical or quantum). The symmetries underlying the geometric model of light are based on the symplectic group. Geometric Optics on Phase Space develops both geometric optics and group theory from first principles in their Hamiltonian formulation on phase space. This treatise provides the mathematical background and also collects a host of useful methods of practical importance, particularly the fractional Fourier transform currently used for image processing. The reader will appreciate the beautiful similarities between Hamilton's mechanics and this approach to optics. The appendices link the geometry thus introduced to wave optics through Lie methods. The book addresses researchers and graduate students.