Geodesic
Stability of isodiametric problem solution in the Minkowski geometry
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (1997) no. 3, pp. 334-338 Cet article a éte moissonné depuis la source Math-Net.Ru

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The theorem is proved: if $(D_B(X)/2)^n-V_B(X)/V_B(B_1)\le\varepsilon$, $0\le\varepsilon$, $V_B(X)=V_B(B_1)$, then $\delta_B(X,B_1)\le2\varepsilon^{1/n}$, where $X$ – convex body in $n$-dimensional space of Minkowski $\tilde M^n$, $B$ – normed body $\tilde M^n$, $B_1=B\cap(-B)$, $V_B(X)$ – diameter $X$, $V_B(X)$ – volume $X$, $\delta_B(X,B_1)$ – deflection of bodies $X$ and $B_1$ in $\tilde M^n$. 
@article{JMAG_1997_4_3_a4,
     author = {V. I. Diskant},
     title = {Stability of isodiametric problem solution in the {Minkowski} geometry},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {334--338},
     year = {1997},
     volume = {4},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1997_4_3_a4/}
}
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V. I. Diskant. Stability of isodiametric problem solution in the Minkowski geometry. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (1997) no. 3, pp. 334-338. http://geodesic.mathdoc.fr/item/JMAG_1997_4_3_a4/