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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.

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Acknowledgements

We would like to thank Tobias Kaiser for helpful discussions. We are grateful to the referee for helpful comments on the manuscript. F.F. would like to thank the Max Planck Institute for Mathematics in the Sciences in Leipzig for hospitality while working on the manuscript. H. vdM.’s work is partially funded by the Excellence Initiative of the German federal and state governments.

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Authors and Affiliations

  1. Department Mathematik, FAU Erlangen-Nürnberg, 91058, Erlangen, Germany

    Lucia Bäuml

  2. Fakultät für Mathematik, Universität Regensburg, 93040, Regensburg, Germany

    Felix Finster

  3. Institut für Mathematik, Universität Innsbruck, 6020, Innsbruck, Austria

    Daniela Schiefeneder

  4. Institut für Mathematik, RWTH Aachen University, 52062, Aachen, Germany

    Heiko von der Mosel

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  1. Lucia Bäuml
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  2. Felix Finster
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  3. Daniela Schiefeneder
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  4. Heiko von der Mosel
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Correspondence to Heiko von der Mosel.

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Communicated by L. Ambrosio.

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Bäuml, L., Finster, F., Schiefeneder, D. et al. Singular support of minimizers of the causal variational principle on the sphere. Calc. Var. 58, 205 (2019). https://doi.org/10.1007/s00526-019-1652-7

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