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Isometric Embedding of Riemannian Manifolds in Euclidean Spaces

Qing HanJia-Xing HongJiaxing Hong

出版	American Mathematical Soc., 2006
主題	Mathematics / Differential Equations / GeneralMathematics / Geometry / AlgebraicMathematics / Geometry / Differential
ISBN	08218407119780821840719
URL	http://books.google.com.hk/books?id=R3rzBwAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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 ${\mathbb R}^3$. 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 Gunther. 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.