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.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…
math.MG2017
Duality of Floating and Illumination Bodies
Olaf Mordhorst, Elisabeth M. Werner
We investigate a duality relation between floating and illumination bodies. The definitions of these two bodies suggest that the polar of the floating body should be similar to the…