A Survey on Classical Minimal Surface Theory

Joaquin Perez (Autor)

Buch | Softcover

182 Seiten

2013
American Mathematical Society (Verlag)
978-0-8218-6912-3 (ISBN)

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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.

William H. Meeks III, University of Massachusetts, Amherst, Amherst, MA, USA Joaquín Pérez, Universidad de Granada, Granada, Spain

Preface
Introduction
Basic results in classical minimal surface theory
Minimal surfaces with finite topology and more than one end
Limits of embedded minimal surfaces without local area or curvature bounds
The structure of minimal laminations of ℝ³
The Ordering Theorem for the space of ends
Conformal structure of minimal surfaces
Uniqueness of the helicoid I: proper case
Embedded minimal annular ends with infinite total curvature
The embedded Calabi–Yau problem
Local pictures, local removable singularities and dynamics
Embedded minimal surfaces of finite genus
Topological aspects of minimal surfaces
Partial results on the Liouville conjecture
The Scherk uniqueness theorem
Calabi–Yau problems
Outstanding problems and conjectures
Bibliography

Reihe/Serie	University Lecture Series
Verlagsort	Providence
Sprache	englisch
Gewicht	348 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-6912-4 / 0821869124
ISBN-13	978-0-8218-6912-3 / 9780821869123
Zustand	Neuware