Minimal Submanifolds And Related Topics
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A01=Yuanlong Xin
Author_Yuanlong Xin
Bernstein Type Theorem
Category=PBMP
Curvature Estimate
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Grassman Manifold
Harmonic Gauss Map
Minimal Submanifold
Parallel Mean Curvature Submanifold
Plateau's Problem
Space-Like Submanifold
Special Lagrangian Submanifold
Stable Minimal Hypersurface
Weierstrass Representation
Product details
- ISBN 9789813236059
- Publication Date: 01 Oct 2018
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
