Let AA be a given compact subset of the euclidean space. We consider the problem of finding a compact connected set SS of minimal 11-dimensional Hausdorff measure, among all compact connected sets containing AA. We prove that when AA is a finite set any minimizer is a finite tree with straight edges, thus recovery the classical Steiner Problem. Analogously, in the case when AA is countable, we prove that every minimizer is a (possibly) countable union of straight segments.

The Steiner problem for infinitely many points

PAOLINI, EMANUELE;
2010-01-01

Abstract

Let AA be a given compact subset of the euclidean space. We consider the problem of finding a compact connected set SS of minimal 11-dimensional Hausdorff measure, among all compact connected sets containing AA. We prove that when AA is a finite set any minimizer is a finite tree with straight edges, thus recovery the classical Steiner Problem. Analogously, in the case when AA is countable, we prove that every minimizer is a (possibly) countable union of straight segments.
2010
Paolini, Emanuele; L., Ulivi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/819627
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