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Search: MSC category 53C65 ( Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx] )

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1. CMB 2007 (vol 50 pp. 474)

Zhou, Jiazu
 On Willmore's Inequality for Submanifolds Let $M$ be an $m$ dimensional submanifold in the Euclidean space ${\mathbf R}^n$ and $H$ be the mean curvature of $M$. We obtain some low geometric estimates of the total square mean curvature $\int_M H^2 d\sigma$. The low bounds are geometric invariants involving the volume of $M$, the total scalar curvature of $M$, the Euler characteristic and the circumscribed ball of $M$. Keywords:submanifold, mean curvature, kinematic formul, scalar curvatureCategories:52A22, 53C65, 51C16
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