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OverviewMinimal 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. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle. Full Product DetailsAuthor: Tobias Holck Colding , William P. Minicozzi IIPublisher: American Mathematical Society Imprint: American Mathematical Society ISBN: 9781470476403ISBN 10: 1470476401 Pages: 313 Publication Date: 28 February 2011 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable  The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsThe 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 Exercises Bibliography Index.ReviewsAuthor InformationTobias Holck Colding, Massachusetts Institute of Technology, Cambridge, MA. William P. Minicozzi II, Johns Hopkins University, Baltimore, MD. Tab Content 6Author Website:Countries AvailableAll regions |
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