# A survey on classical minimal surface theory

- Responsibility
- William H. Meeks III, Joaquín Pérez.
- Language
- English.
- Publication
- Providence, Rhode Island : American Mathematical Society, [2012]
- Physical description
- x, 182 pages : illustrations ; 25 cm.

## Access

## Creators/Contributors

- Author/Creator
- Meeks, William.
- Contributor
- Pérez, Joaquín, 1966-

## Contents/Summary

- Bibliography
- Includes bibliographical references and index.
- Publisher's Summary
- Meeks and Perez 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.

(source: Nielsen Book Data)

## Subjects

- Subject
- Minimal surfaces.
- Differential geometry -- Classical differential geometry -- Minimal surfaces, surfaces with prescribed mean curvature.
- Calculus of variations and optimal control; optimization -- Manifolds -- Minimal surfaces.
- Differential geometry -- Global differential geometry -- Immersions (minimal, prescribed curvature, tight, etc.)

## Bibliographic information

- Publication date
- 2012
- Series
- University lecture series ; volume 60
- ISBN
- 9780821869123 (alk. paper)
- 0821869124 (alk. paper)