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Degree Theory of Immersed Hypersurfaces
Seiten
2021
American Mathematical Society (Verlag)
978-1-4704-4185-2 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-4185-2 (ISBN)
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.
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 $M$.
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 $M$.
Harold Rosenberg, IMPA, Rio de Janeiro, Brazil. Graham Smith, Centre de Recerca Matematica, Barcelona, Spain.
Erscheinungsdatum | 02.07.2020 |
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Reihe/Serie | Memoirs of the American Mathematical Society |
Verlagsort | Providence |
Sprache | englisch |
Maße | 178 x 254 mm |
Gewicht | 145 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
ISBN-10 | 1-4704-4185-3 / 1470441853 |
ISBN-13 | 978-1-4704-4185-2 / 9781470441852 |
Zustand | Neuware |
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