**University Lecture Series**

Volume: 60;
2012;
182 pp;
Softcover

MSC: Primary 53;
Secondary 49

Print ISBN: 978-0-8218-6912-3

Product Code: ULECT/60

List Price: $48.00

Individual Member Price: $38.40

**Electronic ISBN: 978-0-8218-9198-8
Product Code: ULECT/60.E**

List Price: $48.00

Individual Member Price: $38.40

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#### Supplemental Materials

# A Survey on Classical Minimal Surface Theory

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*William H. Meeks, III; Joaquín Pérez*

Meeks and Pérez present a survey of recent spectacular successes in classical minimal surface theory. The classification of minimal planar domains in three-dimensional 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.

#### Table of Contents

# Table of Contents

## A Survey on Classical Minimal Surface Theory

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface ix10 free
- Introduction 112 free
- Basic results in classical minimal surface theory 1324 free
- Minimal surfaces with finite topology and more than one end 4556
- Limits of embedded minimal surfaces without local area or curvature bounds 5364
- The structure of minimal laminations of ℝ³ 7384
- The Ordering Theorem for the space of ends 7788
- Conformal structure of minimal surfaces 8192
- Uniqueness of the helicoid I: proper case 91102
- Embedded minimal annular ends with infinite total curvature 95106
- The embedded Calabi–Yau problem 103114
- Local pictures, local removable singularities and dynamics 113124
- Embedded minimal surfaces of finite genus 123134
- Topological aspects of minimal surfaces 137148
- Partial results on the Liouville conjecture 145156
- The Scherk uniqueness theorem 149160
- Calabi–Yau problems 153164
- Outstanding problems and conjectures 157168
- Bibliography 171182
- Back Cover Back Cover1194

#### Readership

Graduate students and research mathematicians interested in minimal surface theory.