Isometric Embedding of Riemannian Manifolds in Euclidean Spaces

Isometric Embedding of Riemannian Manifolds in Euclidean Spaces pdf epub mobi txt 电子书 下载 2025

出版者:American Mathematical Society
作者:Qing Han
出品人:
页数:260
译者:
出版时间:2006-10-10
价格:USD 77.00
装帧:Hardcover
isbn号码:9780821840719
丛书系列:Mathematical Surveys and Monographs
图书标签:
  • 数学 
  • 微分几何 
  • 几何 
  • 拓扑 
  • 微分几何7 
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The question of the existence of isometric embeddings of Riemannian manifolds in Euclidean space is already more than a century old. This book presents, in a systematic way, results both local and global and in arbitrary dimension but with a focus on the isometric embedding of surfaces in R3. The emphasis is on those PDE techniques which are essential to the most important results of the last century. The classic results in this book include the Janet-Cartan Theorem, Nirenberg's solution of the Weyl problem, and Nash's Embedding Theorem, with a simplified proof by Günther. The book also includes the main results from the past twenty years, both local and global, on the isometric embedding of surfaces in Euclidean 3-space. The work will be indispensable to researchers in the area. Moreover, the authors integrate the results and techniques into a unified whole, providing a good entry point into the area for advanced graduate students or anyone interested in this subject. The authors avoid what is technically complicated. Background knowledge is kept to an essential minimum: a one-semester course in differential geometry and a one-year course in partial differential equations.

http://www.amazon.com/Isometric-Embedding-Riemannian-Mathematical-Monographs/dp/0821840711

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