Overview

Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space, the theory of minimal submanifolds have undergone considerable developments, involving techniques from related areas, such as the analysis of partial differential equations and complex analysis. On the other hand, the relativity theory has led to the study of pseudo-Riemannian manifolds, which turns out to be the most general framework for the study of minimal submanifolds. However, most of the recent books on the subject still present the theory only in the Riemannian case.For the first time, this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian geometry, only assuming from the reader some basic knowledge about manifold theory. Several classical results, such as the Weierstrass representation formula for minimal surfaces, and the minimizing properties of complex submanifolds, are presented in full generality without sacrificing the clarity of exposition. Finally, a number of very recent results on the subject, including the classification of equivariant minimal hypersurfaces in pseudo-Riemannian space forms and the characterization of minimal Lagrangian surfaces in some pseudo-Kahler manifolds are given.

Full Product Details

Author:   Henri Anciaux (Univ Of Sao Paulo, Brazil)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Dimensions:   Width: 15.20cm , Height: 1.30cm , Length: 22.90cm
Weight:   0.417kg
ISBN:  

9789814291248

ISBN 10:   9814291242
Pages:   184
Publication Date:   03 November 2010
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Pseudo-Riemannian Manifolds; Submanifolds; First and Second Variations of Volume; Minimal Submanifolds; Simple Examples of Minimal Surfaces; Weierstrass Representation Formulas for Spacelike and Timelike Minimal Surface in Euclidean Space of Arbitrary Dimension; Equivariant Minimal Hypersurfaces in Space Forms; Pseudo-Kahler Manifolds; Complex and Lagrangian Submanifolds; Examples of Minimal Lagrangian Submanifolds.

Reviews

The book is written in an accessible and quite self-contained way. It is recommendable for a broad audience of students and mathematicians interested in minimal submanifolds in pseudo-Riemannian geometry. -- Mathematical Reviews Mathematical Reviews

The book is written in an accessible and quite self-contained way. It is recommendable for a broad audience of students and mathematicians interested in minimal submanifolds in pseudo-Riemannian geometry. -- Mathematical Reviews ""Mathematical Reviews""

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