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Extreme properties of curves with bounded curvature on a sphere

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.

preprint2016arXivOpen access
Alexander BorisenkoKostiantyn Drach
math.OCmath.DG
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Alexander BorisenkoKostiantyn Drach

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