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

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March 28, 2025 | History

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

Publish Date
Language
English

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Book Details


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 $R 3$

Edition Notes

Published in
Boston

Classifications

Library of Congress
QA

The Physical Object

Pagination
p.

Edition Identifiers

Open Library
OL27035597M
ISBN 10
0821837915
ISBN 13
9780821837917
OCLC/WorldCat
163584531

Work Identifiers

Work ID
OL19846653W

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Download catalog record: RDF / JSON / OPDS | Wikipedia citation
March 28, 2025 Edited by ImportBot Redacting ocaids
July 17, 2022 Edited by ImportBot import existing book
June 30, 2019 Created by MARC Bot Imported from Internet Archive item record