We consider a compact star-shaped mean convex hypersurface. We prove that in some cases the flow exists until it shrinks to a point. We also prove that in the case of a surface of revolution which is star-shaped and mean convex, a smooth solution always exists up to some finite time T < ∞ at which the flow shrinks to a point asymptotically spherically.
|Original language||English (US)|
|Number of pages||29|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Nov 2009|
All Science Journal Classification (ASJC) codes
- Applied Mathematics