Translations of Mathematical Monographs 1991; 142 pp; softcover Volume: 93 Reprint/Revision History: reprinted 2005 ISBN10: 0821837915 ISBN13: 9780821837917 List Price: US$62 Member Price: US$49.60 Order Code: MMONO/93.S
 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, twodimensional surfaces in threedimensional space. The main topics covered are: topological properties of minimal surfaces, stable and unstable minimal films, classical examples, the MorseSmale index of minimal twosurfaces in Euclidean space, and minimal films in Lobachevskian space. Requiring only a standard firstyear calculus and elementary notions of geometry, this book brings the reader rapidly into this fascinating branch of modern geometry. Reviews "Plenty of motivational examples. The prerequisites are kept to a minimum  a large portion of the book should be accessible to undergraduate mathematics students. Clear and elementary proofs coupled with illuminating illustrations make the book pleasant reading."  Mathematical Reviews "Serves as a beautiful introduction to the subject of minimal surfaces."  Zentralblatt MATH Table of Contents  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 twodimensional minimal surfaces in \(R^3\)
