A survey on classical minimal surface theory
 Author/Creator
 Meeks, William.
 Language
 English.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2012]
 Physical description
 x, 182 pages : illustrations ; 25 cm.
Access
Available online

Stacks

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QA644 .M44 2012

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QA644 .M44 2012
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Contributors
 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 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 ColdingMinicozzi 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 CalabiYau 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
 Responsibility
 William H. Meeks III, Joaquín Pérez.
 Series
 University lecture series ; volume 60
 ISBN
 9780821869123 (alk. paper)
 0821869124 (alk. paper)