On Willmore's Inequality for Submanifolds

Zhou, Jiazu

Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 474-480

Résumé

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 $M$ .

Détail

DOI : 10.4153/CMB-2007-047-4

Mots-clés : 52A22, 53C65, 51C16, submanifold, mean curvature, kinematic formula, scalar curvature

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