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Minimal submanifolds and related topics /
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 distribut...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; London :
World Scientific,
©2003.
|
| Colección: | Nankai tracts in mathematics ;
v. 8. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Xin, Y. L., |d 1943- | |
| 245 | 1 | 0 | |a Minimal submanifolds and related topics / |c Yuanlong Xin. |
| 260 | |a Singapore ; |a London : |b World Scientific, |c ©2003. | ||
| 300 | |a 1 online resource (viii, 262 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 490 | 1 | |a Nankai tracts in mathematics ; |v v. 8 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Minimal submanifolds. | |
| 650 | 0 | |a Geometry, Riemannian. | |
| 650 | 6 | |a Sous-variétés minimales. | |
| 650 | 6 | |a Géométrie de Riemann. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Differential. |2 bisacsh | |
| 650 | 0 | 7 | |a Minimal surfaces. |2 cct |
| 650 | 0 | 7 | |a Minimal submanifolds. |2 cct |
| 650 | 7 | |a Geometry, Riemannian. |2 fast |0 (OCoLC)fst00940940 | |
| 650 | 7 | |a Minimal submanifolds. |2 fast |0 (OCoLC)fst01022849 | |
| 776 | 0 | 8 | |i Print version: |a Xin, Y.L., 1943- |t Minimal submanifolds and related topics. |d Singapore ; River Edge, NJ : World Scientific, ©2003 |z 9812386874 |w (OCoLC)54701072 |
| 830 | 0 | |a Nankai tracts in mathematics ; |v v. 8. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=134083 |z Texto completo |
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