Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities
The well known equivalence of the Sobolev inequality and the isoperimetric inequality can be substantially generalized to set up an equivalence of certain other analytic inequalities with geometric inequalities involving Riemannian volume and surface measure. We exploit a special case of these equivalences to give log-Sobolev inequalities for Riemannian manifolds. Some applications to Schrödinger equations are also given.
equivalence of the Sobolev inequality and the isoperimetric
log-Sobolev inequalities for Riemannian manifolds
equivalence of the Sobolev inequality and the isoperimetric inequality
scientific article; zbMATH DE number 3925566