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Isometric Embedding of Riemannian Manifolds in Euclidean Spaces (Mathematical Surveys and Monographs) by Qing Han and Jia-Xing Hong is a nonfiction available to read on EtoBox.

What is Isometric Embedding of Riemannian Manifolds in Euclidean Spaces (Mathematical Surveys and Monographs) about?

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 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 equat

Who reads Isometric Embedding of Riemannian Manifolds in Euclidean Spaces (Mathematical Surveys and Monographs)?

Author

Qing Han and Jia-Xing Hong

Publisher

American Mathematical Society

Published

2006

Language

EN

ISBN

9787419601295

Category

nonfiction

Subjects

Mathematics, Stem