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arxiv: 1002.2860 · v1 · submitted 2010-02-15 · 🧮 math.DG

On strictly convex subsets in negatively curved manifolds

classification 🧮 math.DG
keywords convexsubsetboundarycompleteconnectedcriterioncurvaturecurvatures
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In a complete simply connected Riemannian manifold X of pinched negative curvature, we give a sharp criterion for a subset C to be the epsilon-neighbourhood of some convex subset of X, in terms of the extrinsic curvatures of the boundary of C.

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