- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:48
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2013)
124
2010
0
The Steiner Problem for Infinitely Many Points
Emanuele
Paolini
Università degli Studi di Firenze, FIRENZE, ITALY
L.
Ulivi
Università degli Studi di Firenze, FIRENZE, ITALY
Let A be a given compact subset of the euclidean space. We consider the problem of finding a compact connected set S of minimal 1- dimensional Hausdorff measure, among all compact connected sets containing A. We prove that when A is a finite set any minimizer is a finite tree with straight edges, thus recovering the classical Steiner Problem. Analogously, in the case when A is countable, we prove that every minimizer is a (possibly) countable union of straight segments.
General
$K$-theory
43
56
10.4171/RSMUP/124-3
http://www.ems-ph.org/doi/10.4171/RSMUP/124-3