REAL HYPERSURFACES EVOLVING BY LEVI CURVATURE: SMOOTH REGULARITY OF SOLUTIONS TO THE PARABOLIC LEVI EQUATION

We prove, with a real analysis technique, the smooth regularity of classical solutions to a nonlinear degenerate parabolic PDE with initial data C ^2,α. This equation arises in the study of the geometric properties of the motion by the trace of the Levi form of a real hypersurface in C ² with Levi curvature different from zero at every point and which is locally the graph of a C ^2,α function.