Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator
The authors establish a Lévy-Gromov isoperimetric inequality for the invariant measure of an infinite-dimensional diffusion generator of positive curvature with isoperimetric model the Gaussian measure. This produces in particular a new proof of the Gaussian isoperimetric inequality. This isoperimetric inequality strengthens the classical logarithmic Sobolev inequality in this context. A local version for the heat kernel measures is also proved, which may then be extended into an isoperimetric inequality for the Wiener measure on the paths of a Riemannian manifold with bounded Ricci curvature (Theorem 5.1).
infinite-dimensional diffusion generator
scientific article; zbMATH DE number 856589