Geodesic
One-dimensional Gromov minimal filling problem
Sbornik. Mathematics, Tome 203 (2012) no. 5, pp. 677-726

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to a new branch in the theory of one-dimensional variational problems with branching extremals, the investigation of one-dimensional minimal fillings introduced by the authors. On the one hand, this problem is a one-dimensional version of a generalization of Gromov's minimal fillings problem to the case of stratified manifolds. On the other hand, this problem is interesting in itself and also can be considered as a generalization of another classical problem, the Steiner problem on the construction of a shortest network connecting a given set of terminals. Besides the statement of the problem, we discuss several properties of the minimal fillings and state several conjectures. Bibliography: 38 titles.
Keywords: metric spaces, Gromov minimal fillings, Steiner minimal trees, minimal spanning trees, Steiner ratio. 
@article{SM_2012_203_5_a2,
     author = {A. O. Ivanov and A. A. Tuzhilin},
     title = {One-dimensional {Gromov} minimal filling problem},
     journal = {Sbornik. Mathematics},
     pages = {677--726},
     publisher = {mathdoc},
     volume = {203},
     number = {5},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_5_a2/}
}
TY  - JOUR
AU  - A. O. Ivanov
AU  - A. A. Tuzhilin
TI  - One-dimensional Gromov minimal filling problem
JO  - Sbornik. Mathematics
PY  - 2012
SP  - 677
EP  - 726
VL  - 203
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2012_203_5_a2/
LA  - en
ID  - SM_2012_203_5_a2
ER  - 
%0 Journal Article
%A A. O. Ivanov
%A A. A. Tuzhilin
%T One-dimensional Gromov minimal filling problem
%J Sbornik. Mathematics
%D 2012
%P 677-726
%V 203
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2012_203_5_a2/
%G en
%F SM_2012_203_5_a2
A. O. Ivanov; A. A. Tuzhilin. One-dimensional Gromov minimal filling problem. Sbornik. Mathematics, Tome 203 (2012) no. 5, pp. 677-726. http://geodesic.mathdoc.fr/item/SM_2012_203_5_a2/