Elements of the geometry and topology of minimal surfaces in three-dimensional space

Author(s)

• Fomenko, Anatoliĭ Timofeevich
• Tuzhilin, A. A.

Bibliographic Information

Elements of the geometry and topology of minimal surfaces in three-dimensional space

A.T. Fomenko, A.A. Tuzhilin

（Translations of mathematical monographs, v. 93）

American Mathematical Society, 2005

• : hbk
• : pbk

Other Title

Элементы геометрии и топологии минимальных поверхностей в трехмерном пространстве

Ėlementy geometrii i topologii minimalʹnykh poverkhnosteĭ v trekhmernom prostranstve

Note

Translated from the Russian by E.J.F. Primrose ; tranlation edited by Simeon Ivanov

Reprinted with an errata by the American Mathematical Society, 2005 ; Originally published, c1991

Includes bibliographical references (p. 137-139) and index

Description and Table of Contents

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.

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 two-dimensional minimal surfaces in $R^3$.

by "Nielsen BookData"

Details

• NCID: BA78362295
• ISBN:
  • 0821845527
  • 0821837915
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: rus
• Place of Publication: Providence, R.I.
• Pages/Volumes: vii, 144 p.
• Size: 27 cm
• Classification:
  • LCC : QA644
  • DC20 : 516.3/62
• Subject Headings:
  • LCSH : Surfaces, Minimal
• Parent Bibliography ID:
  • BA00080309