Complete Minimal Surfaces of Finite Total Curvature
By: by Kichoon Yang
Series: Mathematics and Its Applications -- 294; Mathematics and Its Applications -- 294
Publisher: Springer Netherlands
Published: 1994
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 160
ISBN-13: 9789048144433; 9789401711043
Subjects: Functions of complex variables; Global differential geometry; Mathematics; Surfaces (Physics); Crystallography; Geometry, algebraic
Description: This monograph is based on the idea that the study of complete minimal surfaces in R3 of finite total curvature amounts to the study of linear series on algebraic curves. A detailed account of the Puncture Number Problem, which seeks to determine all possible underlying conformal structures for immersed complete minimal surfaces of finite total curvature, is given here for the first time in book form. Several recent results on the puncture number problem are given along with numerous examples. The emphasis is on manufacturing minimal surfaces from a given Riemann surface using the theory of divisions and residue calculus. Relevant results from algebraic geometry are collected in Chapter 1, which makes the book nearly self-contained. A brief survey of minimal surface theory in general is given in Chapter 2. Chapter 3 includes Mo's recent moduli construction. For graduate students and research mathematicians in differential geometry, function theory and algebraic curves, as well as for those working in materials science or crystallography.
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