LAUSR

Abstract In this paper, we consider the motion of a compact, weakly convex hypersurface of revolution Σ 0 ⊂ R n + 1 under the Q k curvature flow. Assume that Σ 0 has a flat side, under a certain non-degeneracy initial condition, we show that Σ t is smooth up to the flat side for t > 0 . Moreover, the interface separating the flat side from the strictly convex side, moves by the Q k − 1 flow until the flat side disappears. We also show that at the focusing time T, i.e., the time when the flat side disappears, the pressure function g is of class C 1 , α , for some α ∈ ( 0 , 1 ) depends on n and k.