Functional inequalities on arbitrary Riemannian manifolds

[摘要] For any connected (not necessarily complete) Riemannian manifold, we construct a probability measure of type e(V(x)) dx, where dx is the Riemannian volume measure and V is a function C-infinity smooth outside a closed set of zero volume, satisfying Poincare-Sobolev type functional inequalities. In particular, V is C-infinity-smooth on the whole manifold when the Poincare and the super-Poincare inequalities are considered. The Sobolev inequality for infinite measures are also studied. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-12-15

[关键词] Riemannian manifolds;Poincare inequality;super-Poincare inequality;log-Sobolev inequality;Sobolev inequality