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.
By:
Yuanlong Xin (Fudan Univ China) Imprint: World Scientific Publishing Co Pte Ltd Country of Publication: Singapore Edition: Second Edition Volume: 16 ISBN:9789813236059 ISBN 10: 9813236051 Series:Nankai Tracts in Mathematics Pages: 396 Publication Date:03 August 2018 Audience:
College/higher education
,
Professional and scholarly
,
Primary
,
Undergraduate
Format:Hardback Publisher's Status: Active
