Geodesic
On Willmore's Inequality for Submanifolds
Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 474-480

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Let $M$ be an $m$ dimensional submanifold in the Euclidean space ${{\text{R}}^{n}}$ and $H$ be the mean curvature of $M$ . We obtain some low geometric estimates of the total squaremean curvature $\int\limits_{M}{{{H}^{2}}d\sigma }$ . 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 $M$ .
DOI : 10.4153/CMB-2007-047-4
Mots-clés : 52A22, 53C65, 51C16, submanifold, mean curvature, kinematic formula, scalar curvature 
Zhou, Jiazu. On Willmore's Inequality for Submanifolds. Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 474-480. doi: 10.4153/CMB-2007-047-4
@article{10_4153_CMB_2007_047_4,
     author = {Zhou, Jiazu},
     title = {On {Willmore's} {Inequality} for {Submanifolds}},
     journal = {Canadian mathematical bulletin},
     pages = {474--480},
     year = {2007},
     volume = {50},
     number = {3},
     doi = {10.4153/CMB-2007-047-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-047-4/}
}
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