Geodesic
Extremal problems for surfaces with bounded absolute (total) mean integral curvature in $n$-dimensionai space
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996), pp. 267-273.

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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. 
@article{JMAG_1996_3_a3,
     author = {V. A. Dolzhenkov},
     title = {Extremal problems for surfaces with bounded absolute (total) mean integral curvature in $n$-dimensionai space},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {267--273},
     publisher = {mathdoc},
     volume = {3},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1996_3_a3/}
}
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V. A. Dolzhenkov. Extremal problems for surfaces with bounded absolute (total) mean integral curvature in $n$-dimensionai space. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996), pp. 267-273. http://geodesic.mathdoc.fr/item/JMAG_1996_3_a3/