8 citations · 65 across the 30 of their papers we have counts for
7 papers · 1 filter
The Topology of the set of line Transversals
Otfried Cheong, Xavier Goaoc, Andreas F. Holmsen
We prove that for any set of pairwise disjoint open convex sets in , the connected components of the set of lines intersecting every member of are co…
Realization spaces of arrangements of convex bodies
Michael Gene Dobbins, Andreas Holmsen, Alfredo Hubard
We introduce combinatorial types of arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our mai…
Cutting convex curves
Andreas F. Holmsen, János Kincses, Edgardo Roldán-Pensado
We show that for any two convex curves and in parametrized by with opposite orientations, there exists a hyperplane with the following propert…
The Colored Hadwiger Transversal Theorem in
Andreas F. Holmsen, Edgardo Roldán-Pensado
Hadwiger's transversal theorem gives necessary and sufficient conditions for a family of convex sets in the plane to have a line transversal. A higher dimensional version was obtai…
Topology of geometric joins
Imre Barany, Andreas F. Holmsen, Roman Karasev
We consider the geometric join of a family of subsets of the Euclidean space. This is a construction frequently used in the (colorful) Carathéodory and Tverberg theorems, and their…
Regular systems of paths and families of convex sets in convex position
Michael G. Dobbins, Andreas F. Holmsen, Alfredo Hubard
In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of eac…