Journal of Convex Analysis 24 (2017), No. 1, 239--259
Copyright Heldermann Verlag 2017
On Holditch's Theorem and Holditch Curves
Harald Proppe
Dept. of Mathematics and Statistics, Concordia University, 1400 De Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada
hal.proppe@concordia.ca
Alina Stancu
Dept. of Mathematics and Statistics, Concordia University, 1400 De Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada
alina.stancu@concordia.ca
Ron J. Stern
Dept. of Mathematics and Statistics, Concordia University, 1400 De Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada
stern@concordia.ca
Holditch's Theorem and results due to A. Broman are revisted and extended under geometric hypotheses. In addition, smoothness and convexity properties of Holditch curves are derived, with emphasis on the necessity of smoothness hypotheses on the parent curve.
Keywords: Holditch's theorem, smoothness and convexity of Holditch curves, convex analysis, Broman's condition, local obtuseness, Mamikon's theorem.
MSC: 26A27, 49J52
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