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 codimensions. 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.
.,." important book for students who are familiar with the fundamentals of Riemannian geometry ..."
Series: Nankai Tracts in Mathematics : Book 8
Number Of Pages: 272
Published: 16th December 2003
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 22.86 x 15.24
Weight (kg): 0.51