10 citations · 49 across the 34 of their papers we have counts for
5 papers · 2 filters
A fractional Helly theorem for boxes
I. Bárány, F. Fodor, A. Martínez-Pérez +3
Let be a family of axis-parallel boxes in and a real number. There exists a real number such that if there are $α{n\choos…
Convex bodies with many elliptic sections
Isaac Arelio, Luis Montejano
{We show in this paper that two normal elliptic sections through every point of the boundary of a smooth convex body essentially characterize an ellipsoid and furthermore, that fou…
A New Topological Helly Theorem and some Transversals Results
Luis Montejano
We prove that for a topological space X with the property that for and every open subset of , a finite family of open sets in has nonempty intersect…
About an Erdős-Grünbaum conjecture concerning piercing of non bounded convex sets
Amanda Montejano, Luis Montejano, Edgardo Roldán-Pensado +1
In this paper, we study the number of compact sets needed in an infinite family of convex sets with a local intersection structure to imply a bound on its piercing number, answerin…
Straight Line motion with rigid sets
Robert Connelly, Luis Montejano
If one is given a rigid triangle in the plane or space, we show that the only motion possible, where each vertex of the triangle moves along a straight line, is given by a hypocycl…