Geodesic
A presentation of the average distance minimizing problem
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XX, Tome 390 (2011), pp. 117-146

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

We talk about the following minimization problem $$ \min F(\Sigma):=\int_\Omega d(x,\Sigma)\,\mathrm d\mu(x), $$ where $\Omega$ is an open subset of $\mathbb R^2$, $\mu$ is a probability measure and where the minimum is taken over all the sets $\Sigma\subset\overline\Omega$ such that $\Sigma$ is compact, connected, and $\mathcal H^1(\Sigma)\leq\alpha_0$ for a given positive constant $\alpha_0$. 
@article{ZNSL_2011_390_a4,
     author = {A. Lemenant},
     title = {A presentation of the average distance minimizing problem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {117--146},
     publisher = {mathdoc},
     volume = {390},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_390_a4/}
}
TY  - JOUR
AU  - A. Lemenant
TI  - A presentation of the average distance minimizing problem
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2011
SP  - 117
EP  - 146
VL  - 390
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2011_390_a4/
LA  - en
ID  - ZNSL_2011_390_a4
ER  - 
%0 Journal Article
%A A. Lemenant
%T A presentation of the average distance minimizing problem
%J Zapiski Nauchnykh Seminarov POMI
%D 2011
%P 117-146
%V 390
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2011_390_a4/
%G en
%F ZNSL_2011_390_a4
A. Lemenant. A presentation of the average distance minimizing problem. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XX, Tome 390 (2011), pp. 117-146. http://geodesic.mathdoc.fr/item/ZNSL_2011_390_a4/