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DOI: 10.23952/cot.2022.13
Received April 14, 2022; Accepted August 23, 2022; Published September 15, 2022
Abstract. An implicit assumption in the original version of Holditch’s theorem is -regularity and strict convexity of the envelope generated by a chord traveling around a convex curve . We establish that this holds when is -regular with positive curvature and the chordlength is sufficiently small. We also consider the case where is polyhedral. Then, strict convexity of the envelope may not hold, but, for sufficiently small chordlength, it is nevertheless -regular. The case of a general convex curve remains an open problem.
How to Cite this Article:
H. Proppe, A. Stancu, R.J. Stern, Holditch’s Envelope, Commun. Optim. Theory 2022 (2022) 13.