Log-Sobolev inequality on non-convex Riemannian manifolds (Q734820): Difference between revisions

Let \(M\) be a connected, non-compact, complete Riemannian manifold with boundary \(\partial M\) and dimension \(d\). In this paper, the author proves log-Sobolev inequality on \(M\) with unbounded non-convex boundaries. The second fundamental form and the curvature take very different roles in the study of such inequalities. The author gave several examples to illustrate this point.