Convex Sets of Constant Width and -diameter

@inproceedings{Minda2007ConvexSO,
  title={Convex Sets of Constant Width and -diameter},
  author={David Minda},
  year={2007}
}
In this article we study -diameterof planarsetsof constantwidth. We obtain analoguesof the isodiametricinequalityandthe Blaschke-LebesgueTheoremfor -diameter of constantwidth sets. Namely, we prove that amongall the setsof given constantwidth, disks have the smallest -diameterand Reuleauxtriangleshave the largest -diameter . We alsodiscuss completesetsaswell assetsof constant -diameter . We show that thereexist infinitely many non-circularsetsof constant -diameterandconstructonesuchset. 1… CONTINUE READING