Complete Minimal Surfaces of Finite Total Curvature

Kichoon Yang (Autor)

Buch | Hardcover

160 Seiten

1994
Springer (Verlag)
978-0-7923-3012-7 (ISBN)

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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.

1. Background Material.- 2. Minimal Surfaces: General Theory.- 3. Minimal Surfaces with Finite Total Curvature.

Erscheint lt. Verlag	31.7.1994
Reihe/Serie	Mathematics and Its Applications ; 294
Reihe/Serie	Mathematics and Its Applications ; 294
Zusatzinfo	VIII, 160 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	156 x 234 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-7923-3012-9 / 0792330129
ISBN-13	978-0-7923-3012-7 / 9780792330127
Zustand	Neuware