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Degree Theory of Immersed Hypersurfaces

Harold Rosenberg
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      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 $M$.
      Format: Paperback / softback CONTRIBUTORS: Harold Rosenberg EAN: 9781470441852 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2020-10-01 CITY: GENRE: MATHEMATICS / Geometry / General, MATHEMATICS / Topology WIDTH: 178 cm SPINE:

      Book Themes:

      Geometry, Topology

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      Harold Rosenberg, IMPA, Rio de Janeiro, Brazil.Graham Smith, Centre de Recerca Matematica, Barcelona, Spain.
      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 $M$.
      Format: Paperback / softback CONTRIBUTORS: Harold Rosenberg EAN: 9781470441852 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2020-10-01 CITY: GENRE: MATHEMATICS / Geometry / General, MATHEMATICS / Topology WIDTH: 178 cm SPINE:

      Book Themes:

      Geometry, Topology

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      Be the first to write a review
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      Harold Rosenberg, IMPA, Rio de Janeiro, Brazil.Graham Smith, Centre de Recerca Matematica, Barcelona, Spain.

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