No. 2018.05

Singular Support of Minimizers of the Causal Variational Principle on the Sphere

*L. BĂ¤uml, F. Finster, D. Schiefeneder, and H. von der Mosel*

Subject: Classical analysis and ODEs, mathematical physics, functional analysis

#### Abstract

The support of minimizing measures of the causal variational principle on the sphere is analyzed. It is proven that in the case $\tau > \sqrt{3}$, the support of every minimizing measure is contained in a finite number of real analytic curves which intersect at a finite number of points. In the case $\tau > \sqrt{6}$ the support is proven to have Hausdorff dimension at most 6/7.