367 citations · 1.6k across the 63 of their papers we have counts for
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From the Mahler conjecture to Gauss linking integrals
Greg Kuperberg
We establish a version of the bottleneck conjecture, which in turn implies a partial solution to the Mahler conjecture on the product $v(K) = (\Vol K)(\Vol K^\circ)$ of the volume…
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…
A generalization of Filliman duality
Greg Kuperberg
Filliman duality expresses (the characteristic measure of) a convex polytope P containing the origin as an alternating sum of simplices that share supporting hyperplanes with P. Th…
Notions of denseness
Greg Kuperberg
The notion of a completely saturated packing [Fejes Toth, Kuperberg and Kuperberg, Highly saturated packings and reduced coverings, Monats. Math. 125 (1998) 127-145] is a sharper v…
The bottleneck conjecture
Greg Kuperberg
The Mahler volume of a centrally symmetric convex body K is defined as M(K)= (Vol K)(Vol K^dual). Mahler conjectured that this volume is minimized when K is a cube. We introduce th…
Circumscribing constant-width bodies with polytopes
Greg Kuperberg
Makeev conjectured that every constant-width body is inscribed in the dual difference body of a regular simplex. We prove that homologically, there are an odd number of such circum…
Another low-technology estimate in convex geometry
Greg Kuperberg
We give a short argument that for some C > 0, every n-dimensional Banach ball K admits a 256-round subquotient of dimension at least C n/(log n). This is a weak version of Milman's…
Highly saturated packings and reduced coverings
Gabor Fejes Tóth, Greg Kuperberg, Włodzimierz Kuperberg
We introduce and study certain notions which might serve as substitutes for maximum density packings and minimum density coverings. A body is a compact connected set which is the c…
Average kissing numbers for non-congruent sphere packings
Greg Kuperberg, Oded Schramm
The Koebe circle packing theorem states that every finite planar graph can be realized as the nerve of a packing of (non-congruent) circles in R^3. We investigate the average kissi…
A low-technology estimate in convex geometry
Greg Kuperberg
Let be an -dimensional symmetric convex body with and let $K\dual$ be its polar body. We present an elementary proof of the fact that $$(\Vol K)(\Vol K\dual)\ge \f…