Given a closed subset Lambda of the open unit ball B-1 subset of R-n for n >= 3, we consider a complete Riemannian metric g on (B) over bar (1)Lambda of constant scalar curvature equal to n( n-1) and conformally related to the Euclidean metric. We prove that every closed Euclidean ball (B) over bar subset of B1 Lambda is convex with respect to the metric g, assuming the mean curvature of the boundary partial derivative B-1 is nonnegative with respect to the inward normal.
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