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A Survey on Classical Minimal Surface Theory
About this Title
William H. Meeks III, University of Massachusetts, Amherst, Amherst, MA and Joaquín Pérez, Universidad de Granada, Granada, Spain
Publication: University Lecture Series
Publication Year:
2012; Volume 60
ISBNs: 978-0-8218-6912-3 (print); 978-0-8218-9198-8 (online)
DOI: https://doi.org/10.1090/ulect/060
MathSciNet review: MR3012474
MSC: Primary 53A10
Table of Contents
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Front/Back Matter
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