Differential Geometry Lectures

Author: Shing-Tung Yau
Publisher:
Publish Date: 2004-12-01
Features: This book is compiled from a series of lectures given by the author and has become a classic work in the field of differential geometry. It is based on topology and algebraic geometry, primarily using analysis as a tool, to discuss certain linear and nonlinear problems in geometry. The book covers topics such as: comparison theorems and gradient estimates, harmonic functions on negatively curved manifolds, eigenvalue problems on Riemannian manifolds, the heat kernel on Riemannian manifolds, conformal deformations of scalar curvature, and locally conformally flat manifolds. The book also includes essays and lectures written by Professor Yau on nonlinear analysis in geometry, unsolved problems in geometry, the future of geometry, a review of geometry and analysis, and the history and prospects of complex geometry. These comprehensive discussions and speeches provide a macro and insightful description of important issues in geometry, showcasing the history and future prospects of the discipline. This book is suitable as a teaching text for senior undergraduate and graduate students in mathematics departments, as well as a reference for teachers and researchers in modern geometry and analysis. The book covers topics such as: comparison theorems and gradient estimates, harmonic functions on negatively curved manifolds, eigenvalue problems on Riemannian manifolds, the heat kernel on Riemannian manifolds, conformal deformations of scalar curvature, and locally conformally flat manifolds.