Geodesic
Filling minimality of Finslerian 2-discs
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, Tome 273 (2011), pp. 192-206

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

We prove that every Riemannian metric on the 2-disc such that all its geodesics are minimal is a minimal filling of its boundary (within the class of fillings homeomorphic to the disc). This improves an earlier result of the author by removing the assumption that the boundary is convex. More generally, we prove this result for Finsler metrics with area defined as the two-dimensional Holmes–Thompson volume. This implies a generalization of Pu's isosystolic inequality to Finsler metrics, both for the Holmes–Thompson and Busemann definitions of the Finsler area. 
@article{TM_2011_273_a6,
     author = {S. V. Ivanov},
     title = {Filling minimality of {Finslerian} 2-discs},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {192--206},
     publisher = {mathdoc},
     volume = {273},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2011_273_a6/}
}
TY  - JOUR
AU  - S. V. Ivanov
TI  - Filling minimality of Finslerian 2-discs
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2011
SP  - 192
EP  - 206
VL  - 273
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2011_273_a6/
LA  - en
ID  - TM_2011_273_a6
ER  - 
%0 Journal Article
%A S. V. Ivanov
%T Filling minimality of Finslerian 2-discs
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2011
%P 192-206
%V 273
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2011_273_a6/
%G en
%F TM_2011_273_a6
S. V. Ivanov. Filling minimality of Finslerian 2-discs. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, Tome 273 (2011), pp. 192-206. http://geodesic.mathdoc.fr/item/TM_2011_273_a6/