Minimal Submanifolds and Related Topics (Second Edition) Contributor(s): Xin, Yuanlong (Author) |
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ISBN: 9813236051 ISBN-13: 9789813236059 Publisher: World Scientific Publishing Company OUR PRICE: $131.10 Product Type: Hardcover - Other Formats Published: October 2018 |
Additional Information |
BISAC Categories: - Mathematics | Geometry - Differential - Mathematics | Topology - General - Mathematics | Differential Equations - General |
Dewey: 516.362 |
LCCN: 2018016992 |
Series: Nankai Tracts in Mathematics |
Physical Information: 0.88" H x 6" W x 9" (1.54 lbs) 396 pages |
Descriptions, Reviews, Etc. |
Publisher 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. |