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A Course in Minimal Surfaces

Tobias Holck Colding Massachusetts Institute of Technology, Cambridge, MA
William P. Minicozzi II Johns Hopkins University, Baltimore, MD
Available Formats:
Hardcover ISBN: 978-0-8218-5323-8
Product Code: GSM/121
List Price: $72.00 MAA Member Price:$64.80
AMS Member Price: $57.60 Electronic ISBN: 978-1-4704-1182-4 Product Code: GSM/121.E List Price:$67.00
MAA Member Price: $60.30 AMS Member Price:$53.60
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List Price: $108.00 MAA Member Price:$97.20
AMS Member Price: $86.40 Click above image for expanded view A Course in Minimal Surfaces Tobias Holck Colding Massachusetts Institute of Technology, Cambridge, MA William P. Minicozzi II Johns Hopkins University, Baltimore, MD Available Formats:  Hardcover ISBN: 978-0-8218-5323-8 Product Code: GSM/121  List Price:$72.00 MAA Member Price: $64.80 AMS Member Price:$57.60
 Electronic ISBN: 978-1-4704-1182-4 Product Code: GSM/121.E
 List Price: $67.00 MAA Member Price:$60.30 AMS Member Price: $53.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$108.00 MAA Member Price: $97.20 AMS Member Price:$86.40
• Book Details

Volume: 1212011; 313 pp
MSC: Primary 49; 53; 58; 57; 35; 83;

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.

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

• Chapters
• Chapter 1. The beginning of the theory
• Chapter 2. Curvature estimates and consequences
• Chapter 3. Weak convergence, compactness and applications
• Chapter 4. Existence results
• Chapter 5. Min-max constructions
• Chapter 6. Embedded solutions of the Plateau problem
• Chapter 7. Minimal surfaces in three-manifolds
• Chapter 8. The structure of embedded minimal surfaces
• Exercises

• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
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Accessibility – to request an alternate format of an AMS title
Volume: 1212011; 313 pp
MSC: Primary 49; 53; 58; 57; 35; 83;

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.

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

• Chapters
• Chapter 1. The beginning of the theory
• Chapter 2. Curvature estimates and consequences
• Chapter 3. Weak convergence, compactness and applications
• Chapter 4. Existence results
• Chapter 5. Min-max constructions
• Chapter 6. Embedded solutions of the Plateau problem
• Chapter 7. Minimal surfaces in three-manifolds
• Chapter 8. The structure of embedded minimal surfaces
• Exercises
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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