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

Buch | Softcover
142 Seiten
2005
American Mathematical Society (Verlag)
978-0-8218-3791-7 (ISBN)
CHF 249,95 inkl. MwSt
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Describes modern and visual aspects of the theory of minimal, two-dimensional surfaces in three-dimensional space. This book covers such topics as topological properties of minimal surfaces, stable and unstable minimal films, classical examples, and the Morse-Smale index of minimal two-surfaces in Euclidean space.
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.

Physical prerequisites: Interfaces between two media The principle of economy in nature Classical minimal surfaces in $R^3$: 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 $R^3$: 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 $R^3$.

Erscheint lt. Verlag 1.5.2007
Reihe/Serie Translations of Mathematical Monographs
Zusatzinfo Illustrations
Verlagsort Providence
Sprache englisch
Gewicht 288 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
Mathematik / Informatik Mathematik Graphentheorie
ISBN-10 0-8218-3791-5 / 0821837915
ISBN-13 978-0-8218-3791-7 / 9780821837917
Zustand Neuware
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