A course in minimal surfaces
"Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis…
Read More ↓Title Statements
- Full title :A course in minimal surfaces / Tobias Holck Colding, William P. Minicozzi II.
Summary
"Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces. This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science."--
Read More ↓Edition Statements
- Publication Date:©2011.
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, R.I
- Language:eng
- Publication Date:©2011.
The Physical Object
- Description:xii, 313 pages : : illustrations (some color) ; : 27 cm.
Edition Identifiers
- ISBN:9780821853238, 0821853236
- oclc:ocn677972650
- LC Classification:QA644
- Dewey Decimal:516.3/62
Table of Contents
The beginning of the theory -- Curvature estimates and consequences -- Weak convergence, compactness and applications -- Existence results -- Min-max constructions -- Embedded solutions of the plateau problem -- Minimal surfaces in three-manifolds -- The structure of embedded minimal surfaces.
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