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Immobilization of smooth convex figures

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Abstract

We establish a curvature criterion to decide whether three points immobilize a plane convex figure with smooth boundary. Then we use it to prove in the affirmative the convex case of Kuperberg's Conjecture. Namely, we prove that any convex figure with smooth boundary, different from a circular disk, can be immobilized with three points.

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Bracho, J., Montejano, L. & Urrutia, J. Immobilization of smooth convex figures. Geom Dedicata 53, 119–131 (1994). https://doi.org/10.1007/BF01264016

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Mathematics Subject Classification (1991)

  • 52A10