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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Rosenberg, H. (Harold), 1941- (Autor), Smith, Graham (Graham Andrew Craig) (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, [2020].
Colección:Memoirs of the American Mathematical Society ; no. 1290.
Temas:
Riemannian manifolds.
Topological degree.
Hypersurfaces.
Curvature.
Variétés de Riemann.
Degré topologique.
Courbure.
Variedades riemannianas
Curvas
Hipersuperficies
Curvature
Hypersurfaces
Riemannian manifolds
Topological degree
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.
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,
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.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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
  • 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

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