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 $6/7$.
Categories: math.CA math-ph math.FA math.MP