Description

Book Synopsis
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 codimension. 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.

Table of Contents
Bernstein's Theorem and Its Generalizations; Weierstrass Type Representations; Plateau's Problem and Douglas-Rato Solution; Minimal Submanifolds of Higher Codimension; Stable Minimal Hypersurfaces; Bernstein Type Theorems for Higher Codimension; Entire Space-Like Submanifolds.

Minimal Submanifolds And Related Topics

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A Hardback by Yuanlong Xin

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    View other formats and editions of Minimal Submanifolds And Related Topics by Yuanlong Xin

    Publisher: World Scientific Publishing Co Pte Ltd
    Publication Date: 16/12/2003
    ISBN13: 9789812386878, 978-9812386878
    ISBN10: 9812386874
    Also in:
    Differential and Riemannian geometry

    Description

    Book Synopsis
    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 codimension. 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.

    Table of Contents
    Bernstein's Theorem and Its Generalizations; Weierstrass Type Representations; Plateau's Problem and Douglas-Rato Solution; Minimal Submanifolds of Higher Codimension; Stable Minimal Hypersurfaces; Bernstein Type Theorems for Higher Codimension; Entire Space-Like Submanifolds.

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