**Graduate Studies in Mathematics**

Volume: 121;
2011;
313 pp;
Hardcover

MSC: Primary 49; 53; 58; 57; 35; 83;

Print ISBN: 978-0-8218-5323-8

Product Code: GSM/121

List Price: $67.00

Individual Member Price: $53.60

**Electronic ISBN: 978-1-4704-1182-4
Product Code: GSM/121.E**

List Price: $67.00

Individual Member Price: $53.60

#### Supplemental Materials

# A Course in Minimal Surfaces

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*Tobias Holck Colding; William P. Minicozzi, II*

Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces.

This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science.

The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.

#### Table of Contents

# Table of Contents

## A Course in Minimal Surfaces

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface ix10 free
- The beginning of the theory 114 free
- Curvature estimates and consequences 6578
- Weak convergence, compactness and applications 105118
- Existence results 133146
- Min-max constructions 163176
- Embedded solutions of the Plateau problem 201214
- Minimal surfaces in three-manifolds 233246
- The structure of embedded minimal surfaces 261274
- Exercises 295308
- Bibliography 299312
- Index 311324 free
- Back Cover Back Cover1330

#### Readership

Graduate students and research mathematicians interested in the theory of minimal surfaces.