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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Constant Mean Curvature Surfaces with Boundary
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Constant Mean Curvature Surfaces with Boundary
Rafael López (Taschenbuch, Englisch)
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Beschreibung
The 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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
23.08.2016
Sprache
Englisch
EAN
9783662512562
Herausgeber
Springer Berlin
Serien- oder Bandtitel
Springer Monographs in Mathematics
Sonderedition
Nein
Autor
Rafael López
Seitenanzahl
292
Einbandart
Taschenbuch
Autorenporträt
R. 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.
Schlagwörter
53, 53A, 53A10, 53C42, 35J, 35J60, Dirichlet problem, flux formula, mean curvature, tangency principle, partial differential equations
Thema-Inhalt
PBMP - Differentielle und Riemannsche Geometrie
PBKJ - Differentialrechnung und -gleichungen
PBM - Geometrie
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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