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Catalogue Information
Field name	Details
Dewey Class	516.36
Title	Complete Minimal Surfaces of Finite Total Curvature ([EBook] /) / by Kichoon Yang.
Author	Yang, Kichoon
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : : Springer Netherlands : : Imprint: Springer, , 1994.
Physical Details	VIII, 160 p. : online resource.
Series	Mathematics and its applications ; 294
ISBN	9789401711043
Summary Note	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.:
Contents note	1. Background Material -- 2. Minimal Surfaces: General Theory -- 3. Minimal Surfaces with Finite Total Curvature.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-017-1104-3
Links to Related Works	Subject References: Algebraic Geometry . Characterization and Evaluation of Materials . Crystallography . Differential Geometry . Functions of a Complex Variable . Functions of complex variables . Materials science . Mathematics . Authors: Yang, Kichoon . Corporate Authors: SpringerLink (Online service) . Series: Mathematics and its applications . Classification: 516.36 .

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Complete Minimal Surfaces of Finite Total Curvature

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