Elements of the Geometry and Topology of Minimal Surfaces in Three-Dimensional Space
A. T. Fomenko(Author)
American Mathematical Society(RI) (Publisher)
Published on 1. January 1991
Book
142 pages
978-0-8218-4552-3 (ISBN)
Description
This book grew out of lectures presented to students of mathematics, physics, and mechanics by A T Fomenko at Moscow University, under the auspices of the Moscow Mathematical Society. The book describes modern and visual aspects of the theory of minimal, two-dimensional surfaces in three-dimensional space. The main topics covered are: topological properties of minimal surfaces, stable and unstable minimal films, classical examples, the Morse-Smale index of minimal two-surfaces in Euclidean space, and minimal films in Lobachevskian space. Requiring only a standard first-year calculus and elementary notions of geometry, this book brings the reader rapidly into this fascinating branch of modern geometry.
More details
Series
Language
English
Place of publication
United States
ISBN-13
978-0-8218-4552-3 (9780821845523)
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Schweitzer Classification
Content
Physical prerequisites: Interfaces between two media; The principle of economy in nature; Classical minimal surfaces in R3: Catenoids; The helicoid; The minimal surface equation, Bernstein's problem, The Scherk surface; Periodic minimal surfaces; Complete minimal surfaces; General properties of minimal surfaces in R3: Isothermal coordinates; Harmonicity and conformality; The Gaussian mapping and the Weierstrass representation; The global Weierstrass representation; Total curvature and complete minimal surfaces; The geometry of complete minimal surfaces of finite total curvature; Indices of two-dimensional minimal surfaces in R3.