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Extreme properties of curves with bounded curvature on a sphere (1605.09157v1)
Published 30 May 2016 in math.DG and math.OC
Abstract: We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded from below. Furthermore, we prove some dual inequalities for convex curves whose curvatures are bounded from above.
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