3 papers
math.FA2020
Fractional perimeters on the sphere
Andreas Kreuml, Olaf Mordhorst
This note treats several problems for the fractional perimeter or -perimeter on the sphere. The spherical fractional isoperimetric inequality is established. It turns out that t…
math.FA2020
The anisotropic fractional isoperimetric problem with respect to unconditional unit balls
Andreas Kreuml
The minimizers of the anisotropic fractional isoperimetric inequality with respect to the convex body in are shown to be equivalent to star bodies whenever i…
math.FA2018
Fractional Sobolev norms and BV functions on manifolds
Andreas Kreuml, Olaf Mordhorst
The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of func…