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Singular Support of Minimizers of the Causal Variational Principle on the Sphere
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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 $6/7$.
Forward citations
Cited by 2 Pith papers
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Energy on spheres and discreteness of minimizing measures
For non-even p, every minimizer of the p-frame energy on the sphere has support with empty interior, and for potentials with finitely many positive Gegenbauer coefficients a discrete minimizer always exists.
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Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts
An expository paper explaining how spacetime and matter can be encoded in a measure on operators and how gravity and quantum theory could emerge from a single action principle.
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