Overview

Differential geometry is a subject related to many fields in mathematics and the sciences. The authors of this book provide a vertically integrated introduction to differential geometry and geometric analysis. The material is presented in three distinct parts: an introduction to geometry via submanifolds of Euclidean space, a first course in Riemannian geometry, and a graduate special topics course in geometric analysis, and it contains more than enough content to serve as a good textbook for a course in any of these three topics. The reader will learn about the classical theory of submanifolds, smooth manifolds, Riemannian comparison geometry, bundles, connections, and curvature, the Chern-Gauss-Bonnet formula, harmonic functions, eigenfunctions, and eigenvalues on Riemannian manifolds, minimal surfaces, the curve shortening flow, and the Ricci flow on surfaces. This will provide a pathway to further topics in geometric analysis such as Ricci flow, used by Hamilton and Perelman to solve the Poincare and Thurston geometrization conjectures, mean curvature flow, and minimal submanifolds. The book is primarily aimed at graduate students in geometric analysis, but it will also be of interest to postdoctoral researchers and established mathematicians looking for a refresher or deeper exploration of the topic.

Full Product Details

Author:   Bennett Chow ,  Yutze Chow
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   245
ISBN:  

9781470477677

ISBN 10:   147047767
Pages:   750
Publication Date:   30 November 2024
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

Geometry of submanifolds of Euclidean space Intuitive introduction to submanifolds in Euclidean space Differential calculus of submanifolds Linearizing submanifolds: Tangent and tensor bundles Curvature and the local geometry of submanifolds Global theorems in the theory of submanifolds Differential topology and Riemannian geometry Smooth manifolds Riemannian manifolds Differential forms and the method of moving frames on manifolds The Gauss-Bonnet and Poincare-Hopf theorems Bundles and the Chern-Gauss-Bonnet formula Elliptic and parabolic equations in geometric analysis Linear elliptic and parabolic equations Elliptic equations and the geometry of minimal surfaces Geometric flows of curves in the plane Uniformization of surfaces via heat flow Bibliography Index

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Author Information

Bennett Chow, University of California, San Diego, La Jolla, CA, and Yutze Chow, University of Wisconsin - Milwaukee, WI.

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