ISBN: 9789048144433

This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature. Our exposition is base… Meer...

This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature. Our exposition is based upon the philosophy that the study of finite total curvature complete minimal surfaces in R3, in large measure, coincides with the study of meromorphic functions and linear series on compact Riemann sur­ faces. This philosophy is first indicated in the fundamental theorem of Chern and Osserman: A complete minimal surface M immersed in R3 is of finite total curvature if and only if M with its induced conformal structure is conformally equivalent to a compact Riemann surface Mg punctured at a finite set E of points and the tangential Gauss map extends to a holomorphic map Mg _ P2. Thus a finite total curvature complete minimal surface in R3 gives rise to a plane algebraic curve. Let Mg denote a fixed but otherwise arbitrary compact Riemann surface of genus g. A positive integer r is called a puncture number for Mg if Mg can be conformally immersed into R3 as a complete finite total curvature minimal surface with exactly r punctures; the set of all puncture numbers for Mg is denoted by P (M ). For example, Jorge and Meeks [JM] showed, by constructing an example g for each r, that every positive integer r is a puncture number for the Riemann surface pl. Trade Books>Trade Paperback>Science>Mathematics>Mathematics, Springer Netherlands Core >1<

ISBN: 9789048144433

This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature. Our exposition is base… Meer...

This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature. Our exposition is based upon the philosophy that the study of finite total curvature complete minimal surfaces in R3, in large measure, coincides with the study of meromorphic functions and linear series on compact Riemann sur­ faces. This philosophy is first indicated in the fundamental theorem of Chern and Osserman: A complete minimal surface M immersed in R3 is of finite total curvature if and only if M with its induced conformal structure is conformally equivalent to a compact Riemann surface Mg punctured at a finite set E of points and the tangential Gauss map extends to a holomorphic map Mg _ P2. Thus a finite total curvature complete minimal surface in R3 gives rise to a plane algebraic curve. Let Mg denote a fixed but otherwise arbitrary compact Riemann surface of genus g. A positive integer r is called a puncture number for Mg if Mg can be conformally immersed into R3 as a complete finite total curvature minimal surface with exactly r punctures; the set of all puncture numbers for Mg is denoted by P (M ). For example, Jorge and Meeks [JM] showed, by constructing an example g for each r, that every positive integer r is a puncture number for the Riemann surface pl. Books > Science & Nature > Math & Physics > Mathematics List_Books<

ISBN: 9789048144433

Paperback, [PU: Springer], This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvat… Meer...

Paperback, [PU: Springer], This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature., Calculus & Mathematical Analysis, Complex Analysis, Complex Variables, Functional Analysis & Transforms, Differential & Riemannian Geometry, Algebraic Geometry, Condensed Matter Physics (liquid State & Solid State Physics), Atomic & Molecular Physics, Materials Science, Testing Of Materials<

2010, ISBN: 9048144434

gebonden uitgave

Softcover reprint of hardcover 1st ed. 1994 Kartoniert / Broschiert Differentielle und Riemannsche Geometrie, Algebraische Geometrie, Werkstoffprüfung, Minimalsurface; Riemannalgebraicv… Meer...

Softcover reprint of hardcover 1st ed. 1994 Kartoniert / Broschiert Differentielle und Riemannsche Geometrie, Algebraische Geometrie, Werkstoffprüfung, Minimalsurface; Riemannalgebraicvarieties; crystallography; differentialgeometry; homology; materialsscience; modulispace, mit Schutzumschlag 11, [PU:Springer Netherlands; Springer Netherland]<

ISBN: 9789048144433

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