Nearly round spheres look convex
نویسندگان
چکیده
We prove that a Riemannian manifold (M, g), close enough to the round sphere in the C topology, has uniformly convex injectivity domains — so M appears uniformly convex in any exponential chart. The proof is based on the Ma–Trudinger–Wang nonlocal curvature tensor, which originates from the regularity theory of optimal transport.
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تاریخ انتشار 2009