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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: Pocket/Paperback
- ISBN: 9781470441852
- Språk: Engelska
- Antal sidor: 62
- Utgivningsdatum: 2021-01-30
- Förlag: American Mathematical Society