Abstract
This paper gives some examples of hypersurfaces ϕt(M n ) 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 2 .
Full Text 
Sign-in/Register to access full text options
Sign-in/Register to access full text options 
Published version (
Free)
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
