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Mat. Fiz. Anal. Geom., 1996, Volume 3, Number 3/4, Pages 267–273 (Mi jmag496)  

Extremal problems for surfaces with bounded absolute (total) mean integral curvature in $n$-dimensionai space

V. A. Dolzhenkov

Kursk State University

Abstract: Some inequalities are proved which relate the absolute mean integral curvature of hypersurface in $n$-dimensional Euclidean space with the volume and diameter of $n$-dimensional body are proved. Lemma of minimality of measure of $(n-1)$-dimenstonal planes set is the focus of attention: hypersphere as the element of set of closed hypersurfaces, bounding the body of fixed volume, has this property.

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Received: 09.06.1994

Citation: V. A. Dolzhenkov, “Extremal problems for surfaces with bounded absolute (total) mean integral curvature in $n$-dimensionai space”, Mat. Fiz. Anal. Geom., 3:3/4 (1996), 267–273

Citation in format AMSBIB
\Bibitem{Dol96}
\by V.~A.~Dolzhenkov
\paper Extremal problems for surfaces with bounded absolute (total) mean integral curvature in $n$-dimensionai space
\jour Mat. Fiz. Anal. Geom.
\yr 1996
\vol 3
\issue 3/4
\pages 267--273
\mathnet{http://mi.mathnet.ru/jmag496}


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