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Softcover ISBN:  9780821869123 
Product Code:  ULECT/60 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9780821891988 
Product Code:  ULECT/60.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9780821869123 
eBook ISBN:  9780821891988 
Product Code:  ULECT/60.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 

Book DetailsUniversity Lecture SeriesVolume: 60; 2012; 182 ppMSC: Primary 53; Secondary 49
Meeks and Pérez present a survey of recent spectacular successes in classical minimal surface theory. The classification of minimal planar domains in threedimensional Euclidean space provides the focus of the account. The proof of the classification depends on the work of many currently active leading mathematicians, thus making contact with much of the most important results in the field. Through the telling of the story of the classification of minimal planar domains, the general mathematician may catch a glimpse of the intrinsic beauty of this theory and the authors' perspective of what is happening at this historical moment in a very classical subject.
This book includes an updated tour through some of the recent advances in the theory, such as Colding–Minicozzi theory, minimal laminations, the ordering theorem for the space of ends, conformal structure of minimal surfaces, minimal annular ends with infinite total curvature, the embedded Calabi–Yau problem, local pictures on the scale of curvature and topology, the local removable singularity theorem, embedded minimal surfaces of finite genus, topological classification of minimal surfaces, uniqueness of Scherk singly periodic minimal surfaces, and outstanding problems and conjectures.
ReadershipGraduate students and research mathematicians interested in minimal surface theory.

Table of Contents

Chapters

Chapter 1. Introduction

Chapter 2. Basic results in classical minimal surface theory

Chapter 3. Minimal surfaces with finite topology and more than one end

Chapter 4. Limits of embedded minimal surfaces without local area or curvature bounds

Chapter 5. The structure of minimal laminations of $\mathbb {R}^3$

Chapter 6. The Ordering Theorem for the space of ends

Chapter 7. Conformal structure of minimal surfaces

Chapter 8. Uniqueness of the helicoid I: proper case

Chapter 9. Embedded minimal annular ends with infinite total curvature

Chapter 10. The embedded Calabi–Yau problem

Chapter 11. Local pictures, local removable singularities and dynamics

Chapter 12. Embedded minimal surfaces of finite genus

Chapter 13. Topological aspects of minimal surfaces

Chapter 14. Partial results on the Liouville conjecture

Chapter 15. The Scherk uniqueness theorem

Chapter 16. Calabi–Yau problems

Chapter 17. Outstanding problems and conjectures


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Meeks and Pérez present a survey of recent spectacular successes in classical minimal surface theory. The classification of minimal planar domains in threedimensional Euclidean space provides the focus of the account. The proof of the classification depends on the work of many currently active leading mathematicians, thus making contact with much of the most important results in the field. Through the telling of the story of the classification of minimal planar domains, the general mathematician may catch a glimpse of the intrinsic beauty of this theory and the authors' perspective of what is happening at this historical moment in a very classical subject.
This book includes an updated tour through some of the recent advances in the theory, such as Colding–Minicozzi theory, minimal laminations, the ordering theorem for the space of ends, conformal structure of minimal surfaces, minimal annular ends with infinite total curvature, the embedded Calabi–Yau problem, local pictures on the scale of curvature and topology, the local removable singularity theorem, embedded minimal surfaces of finite genus, topological classification of minimal surfaces, uniqueness of Scherk singly periodic minimal surfaces, and outstanding problems and conjectures.
Graduate students and research mathematicians interested in minimal surface theory.

Chapters

Chapter 1. Introduction

Chapter 2. Basic results in classical minimal surface theory

Chapter 3. Minimal surfaces with finite topology and more than one end

Chapter 4. Limits of embedded minimal surfaces without local area or curvature bounds

Chapter 5. The structure of minimal laminations of $\mathbb {R}^3$

Chapter 6. The Ordering Theorem for the space of ends

Chapter 7. Conformal structure of minimal surfaces

Chapter 8. Uniqueness of the helicoid I: proper case

Chapter 9. Embedded minimal annular ends with infinite total curvature

Chapter 10. The embedded Calabi–Yau problem

Chapter 11. Local pictures, local removable singularities and dynamics

Chapter 12. Embedded minimal surfaces of finite genus

Chapter 13. Topological aspects of minimal surfaces

Chapter 14. Partial results on the Liouville conjecture

Chapter 15. The Scherk uniqueness theorem

Chapter 16. Calabi–Yau problems

Chapter 17. Outstanding problems and conjectures