The Steiner problem for infinitely many points

E. Paolini; L. Ulivi

Rendiconti del Seminario Matematico della Università di Padova (2010)

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

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Paolini, 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

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  1. [1] L. Ambrosio - P. Tilli, Selected Topics on "Analysis in Metric Spaces", Quaderni della Scuola Normale Superiore, Pisa, 2000. Zbl1084.28500MR2012736
  2. [2] S. Ducret - M. Troyanov, Steiner's invariant and minimal connections, Portugal. Math. (N.S.), 65 (2) (2008), pp. 237--242. Zbl1156.51010MR2428417
  3. [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. [4] A. O. Ivanov - A. A. Tuzhilin, Minimal networks: the Steiner problem and its generalizations, CRC Press, 1994. Zbl0842.90116MR1271779
  5. [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. [6] E. Paolini - E. Stepanov, Existence and regularity for the Steiner problem, http://cvgmt.sns.it/papers/paoste09 (preprint). Zbl1260.49084
  7. [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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