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ON TOTAL MEAN CURVATURES

The Quarterly Journal of Mathematics, 1986
The ith mean curvature \(K_ i\) of a compact immersed submanifold of dimension n in \(E^ k\) is the normalized ith elementary symmetric function of the principal curvatures. The authors consider homothety- invariant integrals of functions of the \(K_ i\). They discuss lower bounds for these.
Kühnel, Wolfgang, Pinkall, Ulrich
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II—mean curvature and weighted mean curvature

Acta Metallurgica et Materialia, 1992
Abstract Several different formulations are in use for mean curvature (appropriate for isotropic surface free energy) and weighted mean curvature (appropriate for anisotropic surface free energy). These formulations are collected and described in this paper.
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On an Inequality of Mean Curvature

Journal of the London Mathematical Society, 1972
where denotes the scalar product in E, cn the area of the unit rc-sphere, and dV the volume element of M. The equality sign of (1) holds when and only when M" is imbedded as a hypersphere in an («+ l)-dimensional subspace of E (Chen [3], [4]; see also Chen [1] and Willmore [6], [7]).
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