A survey on classical minimal surface theory
By: William H. Meeks III, Joaquín Pérez
Contributors: Pérez, Joaquín, 1966-
Series: University lecture series -- Volume 60
Publisher: American Mathematical Society
Published: 2012
Place of publication: Providence, Rhode Island
Language: eng
Number of pages: 182
ISBN-13: 9780821869123
Subjects: Differential geometry -- Classical differential geometry -- Minimal surfaces, surfaces with prescribed mean curvature; Minimal surfaces; Calculus of variations and optimal control; optimization -- Manifolds -- Minimal surfaces; Differential geometry -- Global differential geometry -- Immersions (minimal, prescribed curvature, tight, etc.).
Notes: Includes bibliographical references (pages 171-182).
Table of contents: title: 1. Introduction; title: 2. Basic results in classical minimal surface theory; title: 3. Minimal surfaces with finite topology and more than one end; title: 4. Limits of embedded minimal surfaces without local area or curvature bounds; title: 5. The structure of minimal laminations of R³; title: 6. The Ordering Theorem for the space of ends; title: 7. Conformal structure of minimal surfaces; title: 8. Uniqueness of the Helicoid I: Proper case; title: 9. Embedded minimal annular ends with infinite total curvature; title: 10. The embedded Calabi-Yau problem; title: 11. Local pictures, local removable singularities and dynamics; title: 12. Embedded minimal surfaces of finite genus; title: 13. Topological aspects of minimal surfaces; title: 14. Partial results on the Liouville Conjecture; title: 15. The Scherk Uniqueness Theorem; title: 16. Calabi-Yau problems; title: 17. Outstanding problems and conjectures.