Elements of the Geometry and Topology of Minimal Surfaces in Three-Dimensional Space - Rilegato

Fomenko, A. T.; Tuzhilin, A. A.

Rilegato

ISBN 10: 0821845527 ISBN 13: 9780821845523

Casa editrice: Amer Mathematical Society, 1991

Riassunto

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.

Su questo libro

Contenuti:

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.

Su questa edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 1991
• ISBN 10: 0821845527
• ISBN 13: 9780821845523
• Rilegatura: Copertina rigida