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Some integral formulas for the \((r + 1)\)th mean curvature of a closed hypersurface. (English) Zbl 1250.53007

Summary: By using the operator \(L_r\), we define the notions of \(r\)th order and \(r\)th type of a Euclidean hypersurface. By the use of these notions, we are able to obtain some sharp estimates of the \((r + 1)\)th mean curvature for a closed hypersurface of the Euclidean space in terms of \(r\)th order.

MSC:

53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
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