α-Gauss Curvature flows with flat sides

In this paper, we study the deformation of the 2-dimensional convex surfaces in R3 whose speed at a point on the surface is proportional to α-power of positive part of Gauss Curvature. First, for , we show that there is smooth solution if the initial data is smooth and strictly convex and that there is a viscosity solution with C1,1-estimate before the collapsing time if the initial surface is only convex. Moreover, we show that there is a waiting time effect which means the flat spot of the convex surface will persist for a while. We also show the interface between the flat side and the strictly convex side of the surface remains smooth on 0