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Mat. Fiz. Anal. Geom., 1996, Volume 3, Number 3/4, Pages 261–266 (Mi jmag495)  

Stability of solution of isoperimeter problem in Minkovsky's geometry

V. I. Diskant

Cherkasy State Technological University

Abstract: 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 $\delta_B(X,I)<C\varepsilon^{1/n}$, 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 $B$.

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Received: 23.02.1994

Citation: V. I. Diskant, “Stability of solution of isoperimeter problem in Minkovsky's geometry”, Mat. Fiz. Anal. Geom., 3:3/4 (1996), 261–266

Citation in format AMSBIB
\Bibitem{Dis96}
\by V.~I.~Diskant
\paper Stability of solution of isoperimeter problem in Minkovsky's geometry
\jour Mat. Fiz. Anal. Geom.
\yr 1996
\vol 3
\issue 3/4
\pages 261--266
\mathnet{http://mi.mathnet.ru/jmag495}


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