Convexity in locally conformally flat manifolds with boundary

Details Convexity in locally conformally flat manifolds with boundary Convexity in locally conformally flat manifolds with boundary

2007-11-08

arxiv.org/abs/0711.1250v1

Mathematics

Differential Geometry

8 pages; to appear in Pacific Journal of Mathematics

Scientific paper

Given a closed subset $\La$ of the open unit ball $B_1\subset \real^n$, $n \geq 3$, we will consider a complete Riemannian metric $g$ on $\bar{B_1} \setminus \La$ of constant scalar curvature equal to $n(n-1)$ and conformally related to the Euclidean metric. In this paper we prove that every closed Euclidean ball $\bar{B} \subset B_1\setminus \La$ is convex with respect to the metric $g$, assuming the mean curvature of the boundary $\partial B_1$ is nonnegative with respect to the inward normal.

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