3 citations · 3 across the 6 of their papers we have counts for
4 papers · 1 filter
Lattice packings with gap defects are not completely saturated
Greg Kuperberg, Krystyna Kuperberg, Wlodzimierz Kuperberg
We show that a honeycomb circle packing in with a linear gap defect cannot be completely saturated, no matter how narrow the gap is. The result is motivated by an open probl…
Total curvature and spiralling shortest paths
Imre Barany, Krystyna Kuperberg, Tudor Zamfirescu
This paper gives a partial confirmation of a conjecture of P. Agarwal, S. Har-Peled, M. Sharir, and K. Varadarajan that the total curvature of a shortest path on the boundary of a…
A knotted minimal tree
Krystyna Kuperberg
This paper contains a construction of a finite set X in the boundary of the unit 3-ball in R^3 whose minimal tree is knotted. The example answers Problem 5.17 in ''Problems in Low-…
Almost-tiling the plane by ellipses
Krystyna Kuperberg, Włodzimierz Kuperberg, Jiří Matoušek +1
For any delta > 1 we construct a periodic and locally finite packing of the plane with ellipses whose delta-enlargement covers the whole plane. This answers a question of Imre Bárá…