Nankai Tracts in Mathematics - Vol. 8
MINIMAL SUBMANIFOLDS AND RELATED TOPICS
by Yuanlong Xin (Fudan University, China)
Preface (100k)
Table of Contents (63k)
Chapter 1.1: The Second Fundamental Form (245k)
Chapter 1.2: The First Variational Formula (133k)
Chapter 1.3: Minimal Manifolds in Euclidean Space (134k)
Chapter 1.4: Minimal Submanifolds in the Sphere (136k)
Chapter 1.5: Examples (170k)
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 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.
Contents:
- Bernstein's Theorem and Its Generalizations
- Weierstrass Type
Representations
- Plateau's Problem and Douglas–Rado Solution
- Minimal Submanifolds of Higher Codimension
- Stable Minimal Hypersurfaces
- Bernstein Type Theorems for Higher Codimension
- Entire Space-Like Submanifolds
Readership: Researchers and graduate students in differential geometry.
“This is an important book and is suitable for students who are familiar with the fundamentals of Riemannian geometry, as well as for specialists.”
| 272pp |
Pub. date: Dec 2003 |
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