A fractional isoperimetric problem in the Wiener space

TL;DR

This paper introduces a fractional perimeter concept within an abstract Wiener space and proves that halfspaces uniquely minimize this perimeter under volume constraints.

Contribution

It defines a new fractional perimeter in Wiener spaces and establishes the uniqueness of halfspaces as minimizers under volume constraints.

Findings

Halfspaces are the only volume-constrained minimizers.

A new fractional perimeter concept is introduced in Wiener spaces.

Abstract

We introduce a notion of fractional perimeter in an abstract Wiener space, and we show that halfspaces are the only volume-constrained minimisers.