几何分析最新进展
2009-9
高等教育出版社
李莹英，林长寿，崔茂培 主编
229
"2007 International Conference in Geometric Analysis" was held in TaiwanUniversity from June 18th to 22nd， 2007. This conference is sponsored by Math-ematics Division， Center for Theoretical Sciences （NCTS） Taipei Office， TaidaInstitute for Mathematical Sciences （TIMS）， Academia Sinica， Central Universityand Tsing-Hua University （Xinzu）. Geometric analysis studies functions， maps， tensors， and submanifolds gov-erned by natural differential equations. A good understanding of these objects re-veals important information of analytical and geometric structures， and has manyimplications in physics， algebraic geometry and topology. In recent years， we have witnessed a great success of geometric analysis， themost important event being the solution of the Poincare conjecture by the Ricciflow. This shows the power of geometric partial differential equations in resolvingsome deepest problems in topology.
The launch of this Advanced Lectures in Mathematics series is aimed at keeping mathematicians informed of the latest developments in mathematics, as well as to aid in the learning of new mathematical topics by students all over the world. Each volume consists of either an expository monograph or a collection of significant introductions to important topics. This series emphasizes the history and sources of motivation for the topics under discussion, and also gives an overview of the current status of research in each particular field. These volumes are the first source to which people will turn in order to learn new subjects and to discover the latest results of many cutting-edge fields in mathematics.
PrefaceHuai-Dong Cao: Recent Progress on Ricci SolitonsJianguo Cao, Bo Dai, and Jiaqiang Mei: An Optimal Extension of Perelman's Comparison Theorem for Quadrangles and its ApplicationsDer-Chen Chang and Stephen S.-T. Yau: Geometric Analysis on a Family of Pseudoconvex HypersurfacesShanyu Ji: A New Proof for Faran's Theorem on Maps Between B2 and B3Spiro Karigiannis: Some Notes on G2 and Spin(7) GeometryLei Ni: Closed Type I Ancient Solutions to Ricci FlowJohn Loftin and Mao-Pei Tsui: Limits of Solutions to a Parabolic Monge-Ampere EquationChang-Shou Lin and Chin-Lung Wang: A Function Theoretic View of the Mean Field Equations on ToriSiu-Cheong Lau and Naichung Conan Leung: Conformal Geometry and Special HolonomyLuen-Fai Tam: Exhaustion Functions on Complete ManifoldsSumio Yamada: On Singular Plateau Problem
