ON THE PRESCRIBED MEAN CURVATURE PROBLEM ON THE STANDARD n-DIMENSIONAL BALL

Abstract

Abstract. In this paper, we consider the problem of existence of conformal metrics with prescribed mean curvature on the unit ball of R n , n ≥ 3. Under the assumption that the order of flatness at critical points of prescribed mean curvature function H(x) is β ∈]1, n − 2], we give precise estimates on the losses of the compactness and we prove new existence result through an Euler-Hopf type formula.