Geodesic
Stability of solution of isoperimeter problem in Minkovsky's geometry
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 3, pp. 261-266 
V. I. Diskant. Stability of solution of isoperimeter problem in Minkovsky's geometry. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 3, pp. 261-266. http://geodesic.mathdoc.fr/item/JMAG_1996_3_3_a2/
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     author = {V. I. Diskant},
     title = {Stability of solution of isoperimeter problem in {Minkovsky's} geometry},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {261--266},
     year = {1996},
     volume = {3},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1996_3_3_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $X$ is a convex body in the $n$-dimensional Minkovsky's space $M^n$ ($n\ge2$) with a symmetrical metric, $B$ – normed body of $M^n$, $I$ – isoperimetrix of $M^n$, $F_B(X)$ – area of the surface, $V_B(X)$ – volume of body $X$ in $M^n$. The theorem was proved: there exist such values of $\varepsilon_0>0$, $C>0$, depending on $n$, $r_I$, $R_I$, that if $F_B^n-n^n V_B(I)V_B^{n-1}(X)<\varepsilon$, $0\le\varepsilon<\varepsilon_0$, $V_B(X)= V_B(I)$ it follow that $\delta_B(X,I), where $\delta_B(X,I)$ is deviation of $X$ and $I$ in $M^n$, $r_I$ – a capacity coefficient of $B$ in $I$, $R_I$ – scope coefficient of body $I$ by body $B$.