Type: Article

Line transversals to blown up closed balls

Jerónimo-Castro, Jesús; Roldán-Pensado, Edgardo;

Abstract:

"The number ?d(k) is defined as the minimum ?>0 such that the following holds: For any finite family F={B1,B2,…,Bn} of closed balls in Rd such that every k elements of F have a common line transversal, the elements of the blown up family ?F={?B1,?B2,…,?Bn} have a common line transversal. In this paper we show that ?d(d+1)?4, ?2(4)?22–? and ?2(3)<2.88.''