Disks in Curves of Bounded Convex Curvature
AMERICAN MATHEMATICAL MONTHLY(2020)
摘要
We say that a simple, closed curve gamma in the plane has bounded convex curvature if for every point x on gamma, there is an open unit disk U-x and epsilon(x) > 0 such that x is an element of partial derivative U-x and B-epsilon x(x) boolean AND U-x subset of Int gamma. We prove that the interior of every curve of bounded convex curvature contains an open unit disk.
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