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

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 $6/7$.

arXiv comment26 pages, LaTeX, 3 figures, typos corrected (published version)

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Cited by in corpus (4)

• The Causal Action in Minkowski Space and Surface Layer Integrals
• Spinors on Singular Spaces and the Topology of Causal Fermion Systems
• Causal Fermion Systems and the ETH Approach to Quantum Theory
• Elliptic Methods for Solving the Linearized Field Equations of Causal Variational Principles