Disks in Curves of Bounded Convex Curvature

09/02/2019

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by   Anders Aamand, et al.

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We say that a simple, closed curve γ in the plane has bounded convex curvature if for every point x on γ, there is an open unit disk U_x and ε_x>0 such that x∈∂ U_x and B_ε_x(x)∩ U_x⊂Int γ. We prove that the interior of every curve of bounded convex curvature contains an open unit disk.