Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Holditch's theorem
  • smoothness and convexity of Holditch curves
  • convex analysis
  • Broman's condition
  • local obtuseness
  • Mamikon's theorem

Mathematics Subject Classification

26A27, 49J52

Suggested citation

H. Proppe, A. Stancu, R. J. Stern. “On Holditch's Theorem and Holditch Curves.” Journal of Convex Analysis 24 (2017), No. 1, 239–259.

Copyright Heldermann Verlag 2017