Evolution of hypersurfaces in $ {\Bbb R}^N$ by Gaussian curvature

Abstract.

In this paper we first prove short time existence of a classical solution for the problem which describes the evolution by Gaussian curvature of a strictly convex hypersurface in ${\Bbb R}^N$. Then we give a proof of the existence of a viscosity solution for this problem in such a way as to define a generalized motion existing for each time.