On Willmore's Inequality for Submanifolds

Canadian mathematical bulletin

关键词: submanifold;    mean curvature;    kinematic formul;    scalar curvature;   

DOI  :  10.4153/CMB-2007-047-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $M$ be an $m$ dimensional submanifold in the Euclidean space${mathbf R}^n$ and $H$ be the mean curvature of $M$. We obtainsome low geometric estimates of the total square mean curvature$int_M H^2 dsigma$. The low bounds are geometric invariantsinvolving the volume of $M$, the total scalar curvature of $M$,the Euler characteristic and the circumscribed ball of $M$.

【 授权许可】

Unknown