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OverviewThe study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields. While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of “compact surfaces with boundaries,” narrowing its focus to a geometric view. Basic issues include the discussion whether the symmetries of the curve inherit to the surface; the possible values of the mean curvature, area and volume; stability; the circular boundary case and the existence of the Plateau problem in the non-parametric case. The exposition provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambient spaces. Throughout the text, numerous illustrations clarify the results and their proofs. The book is intended for graduate students and researchers in the field of differential geometry and especially theory of surfaces, including geometric analysis and geometric PDEs. It guides readers up to the state-of-the-art of the theory and introduces them to interesting open problems. Full Product DetailsAuthor: Rafael LópezPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of the original 1st ed. 2013 Dimensions: Width: 15.50cm , Height: 1.70cm , Length: 23.50cm Weight: 4.686kg ISBN: 9783662512562ISBN 10: 3662512564 Pages: 292 Publication Date: 23 August 2016 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Table of ContentsReviewsAuthor InformationR. López, Professor at the University of Granada’s Department of Geometry and Topology has published more than 70 articles, many of them in journals with high Impact Factors (Duke Math. J., J. Diff. Eq. Calculus of Var., Comm. Math. Phys. SIAM J. Math. Anal.) and has served as a visiting professor at Paris VII, Idaho St. Univ., Sao Paulo, Toledo, Iasi and KIAS. His main research area is ‘surfaces with prescribed mean curvature,’ including elliptic equations and general relativity. Tab Content 6Author Website:Countries AvailableAll regions |