A logarithmic Sobolev inequality for closed submanifolds with constant length of mean curvature vector (Q6649701)

In this paper, the authors proved a logarithmic Sobolev inequality. More precisely, such an inequality is proved over a closed \(n\)-dimensional submanifold \(\Sigma\) of \(M\) such that the mean curvature vector \(H\) of \(\Sigma\) satisfies \(|H|=1\). Here \(M\) is a complete and noncompact Riemannian manifold of dimension \(n+m\) with nonnegative sectional curvature and asymptotic volume \(\theta>0\). Further, a necessary and sufficient condition for the equality is also provided.