**Mathematical Surveys and Monographs**

Volume: 130;
2006;
260 pp;
Hardcover

MSC: Primary 35; 53; 58;

Print ISBN: 978-0-8218-4071-9

Product Code: SURV/130

List Price: $81.00

Individual Member Price: $64.80

**Electronic ISBN: 978-1-4704-1357-6
Product Code: SURV/130.E**

List Price: $81.00

Individual Member Price: $64.80

#### Supplemental Materials

# Isometric Embedding of Riemannian Manifolds in Euclidean Spaces

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*Qing Han; Jia-Xing Hong*

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 equations.

#### Table of Contents

# Table of Contents

## Isometric Embedding of Riemannian Manifolds in Euclidean Spaces

- Contents vii8 free
- Preface ix10 free
- A Brief History xi12 free
- Part 1. Isometric Embedding of Riemannian Manifolds 116 free
- Part 2. Local Isometric Embedding of Surfaces in R[sup(3)] 4358
- Part 3. Global Isometric Embedding of Surfaces in R[sup(3)] 143158
- Notes 247262
- Bibliography 249264
- Index 259274

#### Readership

Graduate students and research mathematicians interested in geometric analysis, differential geometry, and PDEs.

#### Reviews

In this book they bring together in a systematic way many recent (and some less recent) results, making the subject more accessible to a wider readership.

-- Mathematical Reviews