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.File in questo prodotto:
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