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Search: All articles in the CMB digital archive with keyword Mean curvature

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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 curvature
Categories:52A22, 53C65, 51C16

2. CMB 2006 (vol 49 pp. 152)

Yun, Jong-Gug
Comparison Geometry With\\$L^1$-Norms of Ricci Curvature
We investigate the geometry of manifolds with bounded Ricci curvature in $L^1$-sense. In particular, we generalize the classical volume comparison theorem to our situation and obtain a generalized sphere theorem.

Keywords:Mean curvature, Ricci curvature

3. CMB 2004 (vol 47 pp. 314)

Yun, Jong-Gug
Mean Curvature Comparison with $L^1$-norms of Ricci Curvature
We prove an analogue of mean curvature comparison theorem in the case where the Ricci curvature below a positive constant is small in $L^1$-norm.

Keywords:mean curvature, Ricci curvature

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