The harmonic mean curvature flow of a 2-dimensional hypersurface.
 Abstract: I will prove some results for the harmonic mean curvature
 flow in a nonconvex case. It is defined by
\frac{dF}{dt} = -\frac{G}{H}\nu and is a fully nonlinear, weakly
 parabolic equation, degenerate at the points at which our
 hypersurface changes its convexity and fast diffusion when H tends
 to zero. We prove a short time existence of such a flow in a
 nonconvex case. We also prove that if H does not go to zero, the
 flow becomes strictly convex at some time and shrinks to a round
point.