caa a22 4500 445813318 CHVBK 20180317145218.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00022-011-0069-z doi (NATIONALLICENCE)springer-10.1007/s00022-011-0069-z Line transversals to blown up closed balls [Elektronische Daten] [Jesús Jerónimo-Castro, Edgardo Roldán-Pensado] The number λ d (k) is defined as the minimum λ>0 such that the following holds: For any finite family $${\mathcal {F}=\{B_1,B_2, \ldots , B_n\}}$$ of closed balls in $${{\mathbb{R}}^d}$$ such that every k elements of $${\mathcal {F}}$$ have a common line transversal, the elements of the blown up family $${\lambda\mathcal {F}=\{\lambda B_1,\lambda B_2, \ldots , \lambda B_n\}}$$ have a common line transversal. In this paper we show that $${\lambda_d(d+1)\leq4, \lambda_2(4)\leq 2\sqrt 2}$$ and λ2(3)<2.88. Springer Basel AG, 2011 Geometric transversal theory nationallicence line transversal nationallicence balls nationallicence Jerónimo-Castro Jesús Facultad de Ingeniería, Universidad Autónoma de Querétaro, Querétaro, México aut Roldán-Pensado Edgardo Department of Mathematics, University College London, WC1E 6BT, London, England aut Journal of Geometry SP Birkhäuser Verlag Basel 100/1-2(2011-04-01), 79-84 0047-2468 100:1-2<79 2011 100 22 https://doi.org/10.1007/s00022-011-0069-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00022-011-0069-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jerónimo-Castro Jesús Facultad de Ingeniería, Universidad Autónoma de Querétaro, Querétaro, México aut NATIONALLICENCE 700 1- Roldán-Pensado Edgardo Department of Mathematics, University College London, WC1E 6BT, London, England aut NATIONALLICENCE 773 0- Journal of Geometry SP Birkhäuser Verlag Basel 100/1-2(2011-04-01), 79-84 0047-2468 100:1-2<79 2011 100 22 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer