Singular support of minimizers of the causal variational principle on the sphere

  • Lucia Bäuml
  • Felix Finster
  • Daniela Schiefeneder
  • Heiko von der MoselEmail author


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.

Mathematics Subject Classification

49Q20 49S05 49N60 58C35 58Z05 28C99 



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Lucia Bäuml
    • 1
  • Felix Finster
    • 2
  • Daniela Schiefeneder
    • 3
  • Heiko von der Mosel
    • 4
    Email author
  1. 1.Department MathematikFAU Erlangen-NürnbergErlangenGermany
  2. 2.Fakultät für MathematikUniversität RegensburgRegensburgGermany
  3. 3.Institut für MathematikUniversität InnsbruckInnsbruckAustria
  4. 4.Institut für MathematikRWTH Aachen UniversityAachenGermany

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