On Willmore's Inequality for Submanifolds

• Autores: Jianzu Zhou
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 50, Nº 3, 2007, págs. 474-480
• Idioma: inglés
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• Resumen

  • Let M be an m dimensional submanifold in the Euclidean space Rn and H be the mean curvature of M. We obtain some low geometric estimates of the total square mean curvature intM H2 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.