# The Steiner problem for infinitely many points

Rendiconti del Seminario Matematico della Università di Padova (2010)

- Volume: 124, page 43-56
- ISSN: 0041-8994

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topPaolini, E., and Ulivi, L.. "The Steiner problem for infinitely many points." Rendiconti del Seminario Matematico della Università di Padova 124 (2010): 43-56. <http://eudml.org/doc/242717>.

@article{Paolini2010,

author = {Paolini, E., Ulivi, L.},

journal = {Rendiconti del Seminario Matematico della Università di Padova},

keywords = {compact connected set of minimal one-dimensional Hausdorff measure; Steiner problem; union of straight segments},

language = {eng},

pages = {43-56},

publisher = {Seminario Matematico of the University of Padua},

title = {The Steiner problem for infinitely many points},

url = {http://eudml.org/doc/242717},

volume = {124},

year = {2010},

}

TY - JOUR

AU - Paolini, E.

AU - Ulivi, L.

TI - The Steiner problem for infinitely many points

JO - Rendiconti del Seminario Matematico della Università di Padova

PY - 2010

PB - Seminario Matematico of the University of Padua

VL - 124

SP - 43

EP - 56

LA - eng

KW - compact connected set of minimal one-dimensional Hausdorff measure; Steiner problem; union of straight segments

UR - http://eudml.org/doc/242717

ER -

## References

top- [1] L. Ambrosio - P. Tilli, Selected Topics on "Analysis in Metric Spaces", Quaderni della Scuola Normale Superiore, Pisa, 2000. Zbl1084.28500MR2012736
- [2] S. Ducret - M. Troyanov, Steiner's invariant and minimal connections, Portugal. Math. (N.S.), 65 (2) (2008), pp. 237--242. Zbl1156.51010MR2428417
- [3] G. Buttazzo - E. Oudet - E. Stepanov, Optimal transportation problems with free Dirichlet regions, Progress in Nonlinear Diff. Equations and their Applications, 51 (2002), pp. 41--65. Zbl1055.49029MR2197837
- [4] A. O. Ivanov - A. A. Tuzhilin, Minimal networks: the Steiner problem and its generalizations, CRC Press, 1994. Zbl0842.90116MR1271779
- [5] M. Miranda, Jr. - E. Paolini - E. Stepanov, On one-dimensional continua uniformly approximating planar sets, Calc. Var. Partial Differential Equations, 27 (3) (2006), pp. 287--309. Zbl1149.49035MR2260804
- [6] E. Paolini - E. Stepanov, Existence and regularity for the Steiner problem, http://cvgmt.sns.it/papers/paoste09 (preprint). Zbl1260.49084
- [7] E. R. Reifenberg, Solution of the Plateau problem for $m$-dimensional surfaces of varying topological type, Acta Math., 104 (1960), pp. 1--92. Zbl0099.08503MR114145

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