Geodesic
Steiner ratio for the Hadamard surfaces of curvature at most~$k0$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 35-51.

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

In this paper, the Hadamard surfaces of curvature at most $k$ are investigated, which are a particular case of Alexandrov surfaces. It was shown that the total angle at the points of an Hadamard surface is not less than $2\pi$. The Steiner ratio of an Hadamard surface was obtained for the case where the surface is unbounded and $k0$. 
@article{FPM_2013_18_2_a2,
     author = {E. A. Zavalnyuk},
     title = {Steiner ratio for the {Hadamard} surfaces of curvature at most~$k<0$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {35--51},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a2/}
}
TY  - JOUR
AU  - E. A. Zavalnyuk
TI  - Steiner ratio for the Hadamard surfaces of curvature at most~$k<0$
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2013
SP  - 35
EP  - 51
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a2/
LA  - ru
ID  - FPM_2013_18_2_a2
ER  - 
%0 Journal Article
%A E. A. Zavalnyuk
%T Steiner ratio for the Hadamard surfaces of curvature at most~$k<0$
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2013
%P 35-51
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a2/
%G ru
%F FPM_2013_18_2_a2
E. A. Zavalnyuk. Steiner ratio for the Hadamard surfaces of curvature at most~$k<0$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 35-51. http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a2/

[1] Aleksandrov A. D., Zalgaller V. A., Dvumernye mnogoobraziya ogranichennoi krivizny, Tr. Mat. in-ta AN SSSR, 63, 1962 | MR | Zbl

[2] Burago D. Yu., Burago Yu. D., Ivanov S. V., Kurs metricheskoi geometrii, In-t kompyuternykh issledovanii, M.–Izhevsk, 2004

[3] Zavalnyuk E. A., “Lokalnaya struktura minimalnykh setei v prostranstvakh Aleksandrova”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika (to appear)

[4] Ivanov A. O., Tuzhilin A. A., “Geometriya minimalnykh setei i odnomernaya problema Plato”, Uspekhi mat. nauk, 47:2 (1992), 53–115 | MR | Zbl

[5] Ivanov A. O., Tuzhilin A. A., Teoriya ekstremalnykh setei, In-t kompyuternykh issledovanii, M.–Izhevsk, 2003

[6] Ivanov A. O., Tuzhilin A. A., Tsislik D., “Otnoshenie Shteinera dlya rimanovykh mnogoobrazii”, Uspekhi mat. nauk, 55:6 (2000), 139–140 | DOI | MR | Zbl

[7] Mischenko V. A., “Otnoshenie Shteinera–Gromova rimanovykh mnogoobrazii”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika (to appear)

[8] Ovsyannikov Z. N., “Otnosheniya Shteinera, Shteinera–Gromova i subotnosheniya Shteinera dlya prostranstva kompaktov v evklidovoi ploskosti s rasstoyaniem Khausdorfa”, Fundament. i prikl. mat., 18:2 (2013), 157–165

[9] Pakhomova A. S., “Kriterii nepreryvnosti otnoshenii tipa Shteinera v prostranstve Gromova–Khausdorfa”, Mat. zametki (to appear)

[10] Pakhomova A. S., “Otsenki dlya subotnosheniya Shteinera i otnosheniya Shteinera–Gromova”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika (to appear)

[11] Cieslik D., “The Steiner ratio of $\mathcal L_{2k}^d$”, Discrete Appl. Math., 95 (1999), 217–221 | DOI | MR | Zbl

[12] Cieslik D., The Steiner Ratio, Kluwer Academic, Boston, 2001 | MR | Zbl

[13] Gao B., Du D. Z., Graham R. L., “A tight lower bound for the Steiner ratio in Minkowski planes”, Discrete Math., 142 (1995), 49–63 | DOI | MR | Zbl

[14] Gilbert E. N., Pollak H. O., “Steiner minimal trees”, SIAM J. Appl. Math., 16:1 (1968), 1–29 | DOI | MR | Zbl

[15] Graham R. L., Hwang F. K., “A remark on Steiner minimal trees”, Bull. Inst. Math. Acad. Sinica, 4 (1976), 177–182 | MR | Zbl

[16] Innami N., Kim B. H., “Steiner ratio for hyperbolic surfaces”, Proc. Japan Acad. Ser. A, 82:6 (2006), 77–80 | DOI | MR | Zbl

[17] Innami N., Naya S., “A comparison theorem for Steiner minimum trees in surfaces with curvature bounded below”, Tôhoku Math. J., 65:1 (2013), 131–157 | DOI | MR | Zbl

[18] Ivanov A., Tuzhilin A., “Differential calculus on the space of Steiner minimal trees in Riemannian manifolds”, Sb. Math., 192:6 (2001), 823–841 | DOI | MR | Zbl

[19] Ivanov A., Tuzhilin A., “The Steiner ratio Gilbert–Pollak conjecture is still open”, Algorithmica, 62:1–2 (2012), 630–632 | DOI | MR | Zbl

[20] Rubinstein J. H., Weng J. F., “Compression theorems and Steiner ratios on spheres”, J. Combin. Opt., 1 (1997), 67–78 | DOI | MR | Zbl