Abstract
This paper gives some examples of hypersurfaces φ(Mn) 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 M2.
Original language | English (US) |
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Pages (from-to) | 701-719 |
Number of pages | 19 |
Journal | Communications in Analysis and Geometry |
Volume | 17 |
Issue number | 4 |
DOIs | |
State | Published - Oct 2009 |