Geodesic
On Some Results in the Geometry of Convex Bodies and their Applications
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 3, pp. 113-123.

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We give a survey of some results in the geometry of convex bodies and their applications.
Keywords: convex body, axial diameter, homothety, projection.
Mots-clés : simplex, interpolation 
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M. V. Nevskii. On Some Results in the Geometry of Convex Bodies and their Applications. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 3, pp. 113-123. http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a7/

[1] M. Lassak, “Approximation of convex bodies by rectangles”, Geom. Dedic., 47 (1993), 111–117 | DOI | MR | Zbl

[2] M. Lassak, “Relationships between widths of a convex body and of an inscribed parallelotope”, Bull. Austral. Math. Soc., 63 (2001), 133–140 | DOI | MR | Zbl

[3] M. Lassak, “Parallelotopes of maximum volume in a simplex”, Discrete Comput. Geom., 21 (1999), 449–462 | DOI | MR | Zbl

[4] H. Martini, “Some characterizing properties of the simplex”, Geom. Dedic., 29 (1989), 1–6 | DOI | MR | Zbl

[5] M. Nevskii, “Properties of axial diameters of a simplex”, Discrete Comput. Geom., 46:2 (2011), 301–312 | DOI | MR | Zbl

[6] K. Radziszewski, “Sur une probleme extremal relatif aux figures inscrites et circonscrites aux fiures convexes”, Ann. Univ. Mariae Curie-Sklodowska. Sect. A, 6 (1952), 5–18 | MR

[7] P. R. Scott, “Lattices and convex sets in space”, Quart. J. Math. Oxford (2), 36 (1985), 359–362 | DOI | MR | Zbl

[8] P. R. Scott, “Properties of axial diameters”, Bull. Austral. Math. Soc., 39 (1989), 329–333 | DOI | MR | Zbl

[9] P. S. Aleksandrov, Kurs analiticheskoi geometrii i lineinoi algebry, Nauka, M., 1979 | MR

[10] V. Blyashke, Krug i shar, Nauka, M., 1967, 232 pp. | MR

[11] E. M. Bronshtein, “Approksimatsiya vypuklykh mnozhestv mnogogrannikami”, Sovremennaya matematika. Fundamentalnye napravleniya, 22 (2007), 5–37 | MR

[12] M. V. Nevskii, “O minimalnoi norme interpolyatsionnogo proektora”, Matematika, kibernetika, informatika, Trudy mezhdunarodnoi nauchnoi konferentsii, posv. pamyati professora A. Yu. Levina, YarGU, Yaroslavl, 2008, 137–144

[13] M. V. Nevskii, “Ob odnom sootnoshenii dlya minimalnoi normy interpolyatsionnogo proektora”, Model. i analiz inform. sistem, 16:2 (2009), 24–43

[14] M. V. Nevskii, “On a property of $n$-dimensional simplices”, Math. Notes, 87:4 (2010), 543–555 | DOI | DOI | MR | Zbl

[15] M. V. Nevskii, “On the axial diameters of a convex body”, Math. Notes, 90:2 (2011), 295–298 | DOI | DOI | MR | Zbl

[16] M. V. Nevskii, “Geometricheskie otsenki v polinomialnoi interpolyatsii”, Model. i analiz inform. sistem, 18:1 (2011), 142–148 | MR

[17] M. V. Nevskii, “O gipoteze Lassaka dlya vypuklogo tela”, Model. i analiz inform. sistem, 18:3 (2011), 5–11

[18] M. Y. Balla, Approximation of convex bodies by parallelotopes, Internal report IC/87/310, International Centre for Theoretical Physics, Trieste, 1987, 5 pp. | Zbl