**Mathematical Surveys and Monographs**

Volume: 130;
2006;
260 pp;

MSC: Primary 35; 53; 58;

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

List Price: $81.00

AMS Member Price: $64.80

MAA Member Price: $72.90

#### 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.

#### Reviews & Endorsements

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

#### 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