A course in minimal surfaces / Tobias Holck Colding, William P. Minicozzi II.
By: Colding, Tobias H.
Contributor(s): Minicozzi, William P.
Material type:
TextSeries: Graduate studies in mathematics: v. 121.Publisher: Providence, R.I. : American Mathematical Society, c2011Description: xii, 313 p. : USD 63.00 ill. (some col.) ; 27 cm.ISBN: 9780821853238 (alk. paper); 0821853236 (alk. paper).Subject(s): Minimal surfaces | Calculus of variations and optimal control; optimization -- Manifolds -- Minimal surfaces | Differential geometry -- Classical differential geometry -- Minimal surfaces, surfaces with prescribed mean curvature | Differential geometry -- Global differential geometry -- Immersions (minimal, prescribed curvature, tight, etc.) | Global analysis, analysis on manifolds -- Variational problems in infinite-dimensional spaces -- Applications to minimal surfaces (problems in two independent variables) | Manifolds and cell complexes -- Low-dimensional topology -- Geometric structures on low-dimensional manifolds | Manifolds and cell complexes -- Topological manifolds -- Topology of general $3$-manifolds | Partial differential equations -- Elliptic equations and systems -- Second-order elliptic equations | Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations. $2 msc | Relativity and gravitational theory -- General relativity -- Black holesDDC classification: 516.3/62 Other classification: 49Q05 | 53A10 | 53C42 | 58E12 | 57M50 | 57N10 | 35J15 | 35J60 | 83C57 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."--
| Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
| Book | Chennai Mathematical Institute General Stacks | 516.362 COL (Browse shelf) | Available | 8585 |
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| 516.362 BRE Ricci flow and the sphere theorem / | 516.362 BUS Convex surfaces / | 516.362 CHE Differential geometry of warped product manifolds and submanifolds / | 516.362 COL A course in minimal surfaces / | 516.362 DAJ Submanifold Theory beyond an introduction. | 516.362 GRO Metric structures for Riemannian and non-Riemannian spaces / | 516.362 HEL Integral geometry and Radon transforms / |
Includes bibliographical references (p. 299-310) and index.
"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."--