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Minimal submanifolds and related topics

Author: Y L Xin
Publisher: River Edge, New Jersey : World Scientific, ©2003.
Series: Nankai tracts in mathematics, v. 8.
Edition/Format:  eBook : Document : EnglishView all editions and formats
Summary:
Annotation The Bernstein problem and the Plateau problem are central topics in the theory of minimal submanifolds. This important book presents the Douglas-Rado solution to the Plateau problem, but the main emphasis is on the Bernstein problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons' work for minimal graphic  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Xin, Y.L., 1943-
Minimal submanifolds and related topics.
River Edge, NJ : World Scientific, ©2003
(OCoLC)54701072
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Y L Xin
ISBN: 9812564381 9789812564382 9812386874 9789812386878
OCLC Number: 123413126
Notes: Based on lectures delivered at the Institute of Mathematics, Fudan University.
Description: 1 online resource (viii, 262 pages) : illustrations.
Contents: Bernstein's theorem and its generalizations --
Weierstrass type representations --
Plateau's problem and Douglas-Rado solution --
Minimal submanifolds of higher codimension --
Stable minimal hypersurfaces --
Bernstein type theorems for higher codimension --
Entire space-like submanifolds.
Series Title: Nankai tracts in mathematics, v. 8.
Responsibility: Yuanlong Xin.

Abstract:

Annotation The Bernstein problem and the Plateau problem are central topics in the theory of minimal submanifolds. This important book presents the Douglas-Rado solution to the Plateau problem, but the main emphasis is on the Bernstein problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons' work for minimal graphic hypersurfaces, and author's own contributions to Bernstein type theorems for higher codimensions. The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds.

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