Minimal submanifolds and related topics

• 作者: Xin, Y. L.,
• 出版: Singapore ;London : World Scientific ©2003.
• 稽核項: 1 online resource (viii, 262 pages) :illustrations.
• 叢書名: Nankai tracts in mathematics ;v. 8
• 標題: Minimal submanifolds. , Geometry, Riemannian. , MATHEMATICS Geometry -- Differential. , GeometryDifferential. , Electronic books. , MATHEMATICS , Minimal surfaces.
• ISBN: 9812386874 , 9789812386878
• ISBN: 9812386874
• 試查全文@TNUA:
  
• 附註: Includes bibliographical references and index. Ch. I. Introduction. 1.1. The second fundamental form. 1.2. The first variational formula. 1.3. Minimal submanifolds in euclidean space. 1.4. Minimal submanifolds in the sphere. 1.5. Examples. 1.6. Rigidity theorems. 1.7. exercises -- ch. II. Bernstein's theorem and its generalizations. 2.1. Gauss map. 2.2. The Weierstrass representation. 2.3. The value distribution of the image under the Gauss map. 2.4. Exercises -- ch. III. Weierstrass type representations. 3.1. The representation for surfaces of prescribed mean curvature. 3.2. The representation for CMC-1 surfaces in [symbol]. 3.3. Exercises -- ch. IV. Plateau's problem and Douglas-Rado solution. 4.1. Mathematical formulation. 4.2. The Dirichlet principle. 4.3. Proof of the main theorem -- ch. V. Minimal submanifolds of higher codimension. 5.1. Kähler geometry and Wirtinger's inequality. 5.2. Special Lagrangian submanifolds. 5.3. Exercises -- ch. VI. Stable minimal hypersurfaces. 6.1. The second variational formula. 6.2. Stable minimal hypersurfaces and applications. 6.3. A classification of certain stable minimal surfaces. 6.4. Stable cone and Bernstein's problem. 6.5. Curvature estimates for minimal hypersurfaces. 6.6. Exercises -- ch. VII. Bernstein type theorems for higher codimension. 7.1. Geometry of Grassmannian manifolds. 7.2. Harmonic Gauss maps. 7.3. Bernstein type theorems -- ch. VIII. Entire space-like submanifolds. 8.1. A Bochner type formula. 8.2. The Gauss image. 8.3. Estimates of the second fundamental form. 8.4. Completeness. 8.5. Bernstein's problem. 8.6. Final remarks.
• 摘要: 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.
• 電子資源: https://dbs.tnua.edu.tw/login?url=https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=134083
• 系統號: 005321581
• 資料類型: 電子書
• 讀者標籤: 需登入
• 引用網址: 複製連結
• 目前引用數