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Degree theory of immersed hypersurfaces /
The authors develop a degree theory for compact immersed hypersurfaces of prescribed K-curvature immersed in a compact, orientable Riemannian manifold, where K is any elliptic curvature function. They apply this theory to count the (algebraic) number of immersed hyperspheres in various cases: where...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
[2020].
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1290. |
| Temas: |
Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15}
> Spaces and manifolds of mappings (including nonlinear versio.
Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15}
> Infinite-dimensional manifolds
> Homotopy and topological q.
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| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
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| 100 | 1 | |a Rosenberg, H. |q (Harold), |d 1941- |e author. |1 https://id.oclc.org/worldcat/entity/E39PBJh4yD6BQJXt9DWgXQgVG3 | |
| 245 | 1 | 0 | |a Degree theory of immersed hypersurfaces / |c Harold Rosenberg, Graham Smith. |
| 264 | 1 | |a Providence : |b American Mathematical Society, |c [2020]. | |
| 264 | 4 | |c ©2020 | |
| 300 | |a 1 online resource (v, 74 pages) | ||
| 334 | |a single unit |2 rdami | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |2 rdaft | ||
| 353 | |a bibliography |b bibliography | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society Ser. ; |v no. 1290 | |
| 588 | 0 | |a Description based on print version record. | |
| 505 | 0 | |a Cover -- Title page -- Chapter 1. Introduction -- 1.1. General -- 1.2. Background -- 1.3. Applications -- Acknowledgments -- Chapter 2. Degree theory -- 2.1. The manifold of immersions and its tangent bundle -- 2.2. Curvature as a vector field -- 2.3. Simplicity -- 2.4. Surjectivity -- 2.5. Finite dimensional sections -- 2.6. Extensions -- 2.7. Orientation -- the finite-dimensional case -- 2.8. Orientation -- the infinite-dimensional case -- 2.9. Constructing the degree -- 2.10. Varying the metric -- Chapter 3. Applications -- 3.1. The generalised Simons' formula | |
| 505 | 8 | |a 3.2. Prescribed mean curvature -- 3.3. Calculating the Degree -- 3.4. Extrinstic Curvature -- 3.5. Special Lagrangian curvature -- 3.6. Extrinsic curvature in two dimensions -- Appendix A. Weakly smooth maps -- Appendix B. Prime immersions -- Bibliography -- Back Cover | |
| 520 | |a The authors develop a degree theory for compact immersed hypersurfaces of prescribed K-curvature immersed in a compact, orientable Riemannian manifold, where K is any elliptic curvature function. They apply this theory to count the (algebraic) number of immersed hyperspheres in various cases: where K is mean curvature, extrinsic curvature and special Lagrangian curvature and show that in all these cases, this number is equal to -\chi(M), where \chi(M) is the Euler characteristic of the ambient manifold M. | ||
| 504 | |a Includes bibliographical references (pages 61-62). | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Riemannian manifolds. | |
| 650 | 0 | |a Topological degree. | |
| 650 | 0 | |a Hypersurfaces. | |
| 650 | 0 | |a Curvature. | |
| 650 | 6 | |a Variétés de Riemann. | |
| 650 | 6 | |a Degré topologique. | |
| 650 | 6 | |a Hypersurfaces. | |
| 650 | 6 | |a Courbure. | |
| 650 | 7 | |a Variedades riemannianas |2 embne | |
| 650 | 7 | |a Curvas |2 embne | |
| 650 | 0 | 7 | |a Hipersuperficies |2 embucm |
| 650 | 7 | |a Curvature |2 fast | |
| 650 | 7 | |a Hypersurfaces |2 fast | |
| 650 | 7 | |a Riemannian manifolds |2 fast | |
| 650 | 7 | |a Topological degree |2 fast | |
| 650 | 7 | |a Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15} -- Spaces and manifolds of mappings (including nonlinear versio. |2 msc | |
| 650 | 7 | |a Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15} -- Infinite-dimensional manifolds -- Homotopy and topological q. |2 msc | |
| 650 | 7 | |a Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15} -- Calculus on manifolds; nonlinear operators [See also 46Txx, |2 msc | |
| 650 | 7 | |a Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15} -- Partial differential equations on manifolds; differential op. |2 msc | |
| 700 | 1 | |a Smith, Graham |q (Graham Andrew Craig), |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjBqfHdjmJVp3CJJQRkBCP | |
| 758 | |i has work: |a Degree theory of immersed hypersurfaces (Text) |1 https://id.oclc.org/worldcat/entity/E39PCH9krgPTxY7Mw3FBxX4Fyq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Rosenberg, Harold |t Degree Theory of Immersed Hypersurfaces |d Providence : American Mathematical Society,c2020 |z 9781470441852 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1290. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=6229940 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH38606887 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL6229940 | ||
| 938 | |a YBP Library Services |b YANK |n 301341941 | ||
| 938 | |a EBSCOhost |b EBSC |n 2504091 | ||
| 994 | |a 92 |b IZTAP | ||