£54.50

Variational Problems in Geometry (Translations of Mathematical Monographs)

Geometry & Topology

Price data last checked 63 day(s) ago - refreshing...

View at Amazon

Price History & Forecast

Last 28 days • 28 data points (No recent data available)

Historical

Generating forecast...

Price Distribution

Price distribution over 28 days • 1 price levels

Days at Price

Price Analysis

Most common price: £55 (28 days, 100.0%)

Price range: £55 - £55

Price levels: 1 different prices over 28 days

Description

A minimal length curve joining two points in a surface is called a geodesic. One may trace the origin of the problem of finding geodesics back to the birth of calculus. Many contemporary mathematical problems, as in the case of geodesics, may be formulated as variational problems in surfaces or in a more generalized form on manifolds. One may characterize geometric variational problems as a field of mathematics that studies global aspects of variational problems relevant in the geometry and topology of manifolds. For example, the problem of finding a surface of minimal area spanning a given frame of wire originally appeared as a mathematical model for soap films. It has also been actively investigated as a geometric variational problem. With recent developments in computer graphics, totally new aspects of the study on the subject have begun to emerge.This book is intended to be an introduction to some of the fundamental questions and results in geometric variational problems, studying variational problems on the length of curves and the energy of maps. The first two chapters treat variational problems of the length and energy of curves in Riemannian manifolds, with an in-depth discussion of the existence and properties of geodesics viewed as solutions to variational problems. In addition, a special emphasis is placed on the facts that concepts of connection and covariant differentiation are naturally induced from the formula for the first variation in this problem, and that the notion of curvature is obtained from the formula for the second variation.The last two chapters treat the variational problem on the energy of maps between two Riemannian manifolds and its solution, harmonic maps. The concept of a harmonic map includes geodesics and minimal submanifolds as examples. Its existence and properties have successfully been applied to various problems in geometry and topology. The author discusses in detail the existence theorem of Eells-Sampson, which is considered to be the most fundamental among existence theorems for harmonic maps. The proof uses the inverse function theorem for Banach spaces. It is presented to be as self-contained as possible for easy reading.Each chapter may be read independently, with minimal preparation for covariant differentiation and curvature on manifolds. The first two chapters provide readers with basic knowledge of Riemannian manifolds. Prerequisites for reading this book include elementary facts in the theory of manifolds and functional analysis, which are included in the form of appendices. Exercises are given at the end of each chapter. This is the English translation of a book originally published in Japanese. It is an outgrowth of lectures delivered at Tohoku University and at the Summer Graduate Program held at the Institute for Mathematics and its Applications at the University of Minnesota. It would make a suitable textbook for advanced undergraduates and graduate students. This item will also be of interest to those working in analysis.

Key Features

Used Book in Good Condition

Product Specifications

Format: paperback
ASIN: 0821813560
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Geometry & Topology
Domain: Amazon UK
Release Date: 26 September 2002
Listed Since: 21 December 2006

Barcode

No barcode data available

Variational Problems in Geometry (Translations of Mathematical Monographs)

Price History & Forecast

Price Distribution

Price Analysis

Description

Key Features

Product Specifications

Barcode

Similar Products You Might Like

Analysis Of Harmonic Maps And Their Heat Flows, The

Geometry of Manifolds (AMS Chelsea Publishing) (Chelsea Publications)

C*-Algebras and Elliptic Operators in Differential Topology: 192 (Translations of Mathematical Monographs)

Basic Algebraic Geometry (Springer Study Edition)

Curves and Surfaces (Graduate Studies in Mathematics): 2nd Edition

Geometry VI: Riemannian Geometry: 91 (Encyclopaedia of Mathematical Sciences, 91)

Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics)

Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees: Applications to Non-Archimedean Diophantine Approximation: 329 (Progress in Mathematics, 329)

Functional Inequalities: New Perspectives and New Applications (Mathematical Surveys and Monographs)

Minimal Surfaces, Stratified Multivarifolds, and the Plateau Problem (Translations of Mathematical Monographs)

Nonlinear Analysis on Manifolds. Monge-Ampère Equations: 252 (Grundlehren der mathematischen Wissenschaften, 252)

Advances in Moduli Theory (Translations of Mathematical Monographs (Iwanami Series in Modern Mathematics))

Translation Surfaces: 242 (Graduate Studies in Mathematics)

Translation Surfaces: 242 (Graduate Studies in Mathematics)

Geometrical Dynamics of Complex Systems: A Unified Modelling Approach to Physics, Control, Biomechanics, Neurodynamics and Psycho-Socio-Economical ... and Automation: Science and Engineering, 31)

Harmonic Analysis on Commutative Spaces (Mathematical Surveys & Monographs)

Cartesian Currents in the Calculus of Variations II: Variational Integrals: 38 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 38)

Differential Geometry Of Curves And Surfaces With Singularities: 1 (Series In Algebraic And Differential Geometry)

LECTURES ON THE GEOMETRY OF MANIFOLDS (2ND EDITION)

Global Analysis: Differential Forms in Analysis, Geometry and Physics (Graduate Studies in Mathematics)

Elementary Geometry in Hyperbolic Space: 11 (De Gruyter Studies in Mathematics, 11)

Geometry of Differential Forms (Translations of Mathematical Monographs (Iwanami Series in Modern Mathematics))

Differential Geometry Of Curves And Surfaces

Lectures on Analytic Differential Equations (Graduate Studies in Mathematics)