Examples of hypersurfaces flowing by curvature in a Riemannian manifold
نویسندگان
چکیده
This paper gives some examples of hypersurfaces φt(M ) evolving in time with speed determined by functions of the normal curvatures in an (n+ 1)-dimensional hyperbolic manifold; we emphasize the case of flow by harmonic mean curvature. The examples converge to a totally geodesic submanifold of any dimension from 1 to n, and include cases which exist for infinite time. Convergence to a point was studied by Andrews, and only occurs in finite time. For dimension n = 2, the destiny of any harmonic mean curvature flow is strongly influenced by the genus of the surface M. Mathematics Subject Classification: 35K15, 53C44
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