Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces

TL;DR

This paper investigates the properties of the Ornstein-Uhlenbeck semigroup in infinite-dimensional Gaussian spaces, focusing on the concentration of surface measure on points of density 1/2 for sets of finite perimeter.

Contribution

It extends finite-dimensional geometric measure theory to infinite-dimensional Gaussian spaces by characterizing surface measures via the Ornstein-Uhlenbeck semigroup.

Findings

Surface measure concentrates on points of density 1/2

Density is characterized through the Ornstein-Uhlenbeck semigroup

Results generalize finite-dimensional geometric measure theory

Abstract

We study points of density 1/2 of sets of finite perimeter in infinite-dimensional Gaussian spaces and prove that, as in the finite-dimensional theory, the surface measure is concentrated on this class of points. Here density 1/2 is formulated in terms of the pointwise behaviour of the Ornstein-Uhlembeck semigroup.