Geodesic
On the $P$-Property of Compact Convex Sets
Matematičeskie zametki, Tome 71 (2002) no. 3, pp. 323-333 
M. V. Balashov. On the $P$-Property of Compact Convex Sets. Matematičeskie zametki, Tome 71 (2002) no. 3, pp. 323-333. http://geodesic.mathdoc.fr/item/MZM_2002_71_3_a0/
@article{MZM_2002_71_3_a0,
     author = {M. V. Balashov},
     title = {On the $P${-Property} of {Compact} {Convex} {Sets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--333},
     year = {2002},
     volume = {71},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_3_a0/}
}
TY  - JOUR
AU  - M. V. Balashov
TI  - On the $P$-Property of Compact Convex Sets
JO  - Matematičeskie zametki
PY  - 2002
SP  - 323
EP  - 333
VL  - 71
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_71_3_a0/
LA  - ru
ID  - MZM_2002_71_3_a0
ER  - 
%0 Journal Article
%A M. V. Balashov
%T On the $P$-Property of Compact Convex Sets
%J Matematičeskie zametki
%D 2002
%P 323-333
%V 71
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_2002_71_3_a0/
%G ru
%F MZM_2002_71_3_a0

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

Compact convex sets with a special property ($P$-property) in a finite-dimensional space are considered. This property ensures a certain regularity of the boundaries of such sets. A fairly complete description of the class of compact convex sets with the $P$-property is given. It is shown that this class is closed with respect to the basic set operations. The application of the $P$-property is exemplified; in particular, it is shown that any generating set has the $P$-property.

[1] Rokafellar R. T., Vypuklyi analiz, Mir, M., 1973

[2] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974 | Zbl

[3] Balashov M. V., Polovinkin E. S., “$M$-silno vypuklye podmnozhestva i ikh porozhdayuschie mnozhestva”, Matem. sb., 191:1 (2000), 26–64 | MR

[4] Ivanov G. E., Polovinkin E. S., “O silno vypuklykh lineinykh differentsialnykh igrakh”, Differents. uravneniya, 31:10 (1995), 1641–1648 | MR | Zbl

[5] Polovinkin E. S., “Silno vypuklyi analiz”, Matem. sb., 187:2 (1996), 103–130 | MR | Zbl

[6] Polovinkin E. S., Elementy teorii mnogoznachnykh otobrazhenii, Uchebn. posobie, Izd. MFTI, M., 1982

[7] Balashov M. V., “O geometricheskoi raznosti mnogoznachnykh otobrazhenii”, Matem. zametki, 70:2 (2001), 163–169 | MR | Zbl