Geodesic
Unit Disk of the Smallest Self-Perimeter in a Minkowski Plane
Matematičeskie zametki, Tome 81 (2007) no. 1, pp. 125-135.

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On a Minkowski plane with nonsymmetric metric, we find all unit disks with self-perimeter 6, the smallest possible value.
Keywords: Minkowski plane, nonsymmetric metric, self-perimeter. 
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A. I. Shcherba. Unit Disk of the Smallest Self-Perimeter in a Minkowski Plane. Matematičeskie zametki, Tome 81 (2007) no. 1, pp. 125-135. http://geodesic.mathdoc.fr/item/MZM_2007_81_1_a9/

[1] H. Minkowski, Geometrie der Zahlen, Leipzig–Berlin, 1910 | Zbl

[2] T. Bonnezen, V. Fenkhel, Teoriya vypuklykh tel, Fazis, M., 2002 | MR | Zbl

[3] V. A. Sadovnichii, Teoriya operatorov, Izd-vo Mosk. un-ta, M., 1986 | MR | Zbl

[4] K. Leikhtveis, Vypuklye mnozhestva, Nauka, M., 1985 | MR | Zbl

[5] V. I. Diskant, “Utochnenie izodiametralnogo neravenstva v geometrii Minkovskogo”, Matem. fizika, analiz, geometriya, 1:2 (1994), 216–226 | MR | Zbl

[6] A. C. Thompson, Minkowski Geometry, Cambridge University Press, Cambridge, 1996 | MR | Zbl

[7] S. Golab, “Quelques problèmes métriques de la géométrie de Minkowski”, Trav. l'Acad. Mines Cracovie, 6 (1932), 1–79 | MR | Zbl

[8] Yu. G. Reshetnyak, “Odna ekstremalnaya zadacha iz teorii vypuklykh krivykh”, UMN, 8:6 (1953), 125–126 | MR | Zbl

[9] D. Laugwitz, “Konvexe Mittelpunktsbereiche und normierte Raume”, Math. Z., 61 (1954), 235–244 | DOI | MR | Zbl

[10] J. J. Schäffer, “Inner diameter, perimeter, and girth of spheres”, Math. Ann., 173 (1967), 59–79 | DOI | MR | Zbl

[11] A. I. Scherba, “Ob otsenke perimetra edinichnogo kruga na ploskosti Minkovskogo”, Tr. Rubtsovskogo industrialnogo in-ta, 2003, no. 12, 96–107 | Zbl

[12] B. Grünbaum, “The perimeter of Minkowski unit discs”, Colloq. Math., 15 (1966), 135–139 | MR | Zbl

[13] B. Grünbaum, “Self-circumference of convex sets”, Colloq. Math., 13 (1964), 55–57 | MR | Zbl

[14] V. V. Makeev, “Ob otsenke sverkhu perimetra nesimmetrichnogo edinichnogo kruga na ploskosti Minkovskogo”, Zap. nauchn. semin. POMI, 299, 2003, 262–266 | MR