By studying a fully nonlinear flow deforming conformal metrics on a compact and connected manifold, we prove the long time existence and the exponential convergence of the solutions of the flow for any initial metric g0 with the Schouten tensor Ag0 ∈ Γk.
This paper proposes a new method for the construction of Bernstein-Bezier algebraic hypersurface on a simplex with prescribed topology. The method is based on the combinatorial patchworking of Viro method. The topology of the Viro Bernstein-Bezier algebraic hypersurface piece is also described.
