Given a complete metric space X and a compact set C⊂X , the famous Steiner (or minimal connection) problem is that of finding a set S of minimum length (one-dimensional Hausdorff measure ℋ¹) ) among the class of sets St(C):={S⊂X:S∪C isconnected}. In this paper we provide conditions on existence of minimizers and study topological regularity results for solutions of this problem. We also study the relationships between several similar variants of the Steiner problem. At last, we provide some applications to locally minimal sets.
Existence and regularity results for the Steiner problem
PAOLINI, EMANUELE;E. STEPANOV
2013-01-01
Abstract
Given a complete metric space X and a compact set C⊂X , the famous Steiner (or minimal connection) problem is that of finding a set S of minimum length (one-dimensional Hausdorff measure ℋ¹) ) among the class of sets St(C):={S⊂X:S∪C isconnected}. In this paper we provide conditions on existence of minimizers and study topological regularity results for solutions of this problem. We also study the relationships between several similar variants of the Steiner problem. At last, we provide some applications to locally minimal sets.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
PaoSte12a.pdf
solo utenti autorizzati
Tipologia:
Versione finale editoriale
Licenza:
NON PUBBLICO - accesso privato/ristretto
Dimensione
1.04 MB
Formato
Adobe PDF
|
1.04 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
|
final-for-CalcVar.pdf
accesso aperto
Tipologia:
Documento in Post-print
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
354.27 kB
Formato
Adobe PDF
|
354.27 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
