scholarly journals Irregularities of distribution and geometry of planar convex sets

2022 ◽  
Vol 396 ◽  
pp. 108162
Author(s):  
Luca Brandolini ◽  
Giancarlo Travaglini
Keyword(s):  
Convex Sets ◽  
Planar Convex ◽  
Irregularities Of Distribution

scholarly journals Maximizing the overlap of two planar convex sets under rigid motions

2007 ◽  
Vol 37 (1) ◽  
pp. 3-15 ◽  
Author(s):  
Hee-Kap Ahn ◽  
Otfried Cheong ◽  
Chong-Dae Park ◽  
Chan-Su Shin ◽  
Antoine Vigneron
Keyword(s):  
Convex Sets ◽  
Planar Convex ◽  
Rigid Motions

Translations of planar convex sets

1971 ◽  
Vol 22 (1) ◽  
pp. 103-105 ◽  
Author(s):  
Togo Nishiura ◽  
Franz Schnitzer
Keyword(s):  
Convex Sets ◽  
Planar Convex

scholarly journals New inequalities for planar convex sets with lattice point constraints

1996 ◽  
Vol 54 (3) ◽  
pp. 391-396 ◽  
Author(s):  
Poh W. Awyong ◽  
Paul R. Scott
Keyword(s):  
Lattice Point ◽  
Convex Sets ◽  
Convex Set ◽  
Integral Lattice ◽  
Planar Convex ◽  
New Inequalities

We obtain new inequalities relating the inradius of a planar convex set with interior containing no point of the integral lattice, with the area, perimeter and diameter of the set. By considering a special sublattice of the integral lattice, we also obtain an inequality concerning the inradius and area of a planar convex set with interior containing exactly one point of the integral lattice.

scholarly journals Petruska’s question on planar convex sets

2020 ◽  
Vol 343 (9) ◽  
pp. 111956
Author(s):  
Adam S. Jobson ◽  
André E. Kézdy ◽  
Jenő Lehel ◽  
Timothy J. Pervenecki ◽  
Géza Tóth
Keyword(s):  
Convex Sets ◽  
Planar Convex

Some Inequalities Related to Planar Convex Sets

1982 ◽  
Vol 25 (3) ◽  
pp. 302-310 ◽  
Author(s):  
R. J. Gardner ◽  
S. Kwapien ◽  
D. P. Laurie
Keyword(s):  
Convex Subset ◽  
Convex Sets ◽  
Compact Convex ◽  
Compact Convex Subset ◽  
Planar Convex

AbstractB. Grünbaum and J. N. Lillington have considered inequalities defined by three lines meeting in a compact convex subset of the plane. We prove a conjecture of Lillington and propose some conjectures of our own.

scholarly journals Adaptive estimation of planar convex sets

2018 ◽  
Vol 46 (3) ◽  
pp. 1018-1049
Author(s):  
T. Tony Cai ◽  
Adityanand Guntuboyina ◽  
Yuting Wei
Keyword(s):  
Convex Sets ◽  
Adaptive Estimation ◽  
Planar Convex

scholarly journals Some inequalities for planar convex sets containing one lattice point

1998 ◽  
Vol 58 (1) ◽  
pp. 159-166
Author(s):  
M. A. Hernández Cifre ◽  
S. Segura Gomis
Keyword(s):  
Lattice Point ◽  
Convex Sets ◽  
Convex Set ◽  
Integer Lattice ◽  
Minimal Width ◽  
Planar Convex

We obtain two inequalities relating the diameter and the (minimal) width with the area of a planar convex set containing exactly one point of the integer lattice in its interior. They are best possible. We then use these results to obtain some related inequalities.

scholarly journals Circumradius-diameter and width-inradius relations for lattice constrained convex sets

1999 ◽  
Vol 59 (1) ◽  
pp. 147-152 ◽  
Author(s):  
Poh Wah Awyong ◽  
Paul R. Scott
Keyword(s):  
Lattice Point ◽  
Convex Sets ◽  
Convex Set ◽  
Compact Convex ◽  
Integer Lattice ◽  
Lattice Points ◽  
Compact Convex Set ◽  
Planar Convex ◽  
Rectangular Lattices

Let K be a planar, compact, convex set with circumradius R, diameter d, width w and inradius r, and containing no points of the integer lattice. We generalise inequalities concerning the ‘dual’ quantities (2R − d) and (w − 2r) to rectangular lattices. We then use these results to obtain corresponding inequalities for a planar convex set with two interior lattice points. Finally, we conjecture corresponding results for sets containing one interior lattice point.

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