
Minimal Submanifolds And Related Topics
Yuanlong Xin(Author)
World Scientific Publishing Co Pte Ltd
Published on 1. October 2018
Book
Hardback
396 pages
978-981-323-605-9 (ISBN)
Description
In the theory of minimal submanifolds, Bernstein's problem and Plateau's problem are central topics. This important book presents the Douglas-Rado solution to Plateau's problem, but the main emphasis is on Bernstein's 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 the 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.This new edition contains the author's recent work on the Lawson-Osserman's problem for higher codimension, and on Chern's problem for minimal hypersurfaces in the sphere. Both Chern's problem and Lawson-Osserman's problem are important problems in minimal surface theory which are still unsolved. In addition, some new techniques were developed to address those problems in detail, which are of interest in the field of geometric analysis.
More details
Series
Edition
Second Edition
Language
English
Place of publication
Singapore
Singapore
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 26 mm
Weight
725 gr
ISBN-13
978-981-323-605-9 (9789813236059)
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Schweitzer Classification