Description
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.
About the Author
Bennett Chow, University of California, San Diego, La Jolla, CA, and Yutze Chow, University of Wisconsin - Milwaukee, WI.
Book Information
ISBN 9781470478049
Author Bennett Chow
Format Paperback
Page Count 750
Imprint American Mathematical Society
Publisher American Mathematical Society