Finster, Felix; Schiefeneder, Daniela On the support of minimizers of causal variational principles. (English) Zbl 1306.49060 Arch. Ration. Mech. Anal. 210, No. 2, 321-364 (2013). Authors’ abstract: A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or it is singular in the sense that its interior is empty. In the examples of the circle, the sphere and certain flag manifolds, the general results are supplemented by a more detailed and explicit analysis of the minimizers. On the sphere, we get a connection to packing problems and the Tammes distribution. Moreover, the minimal action is estimated from above and below. Reviewer: Antonio Masiello (Bari) Cited in 18 Documents MSC: 49Q20 Variational problems in a geometric measure-theoretic setting 49S05 Variational principles of physics 81T99 Quantum field theory; related classical field theories Keywords:causal variational principles; minimizing measures; relativistic quantum field theory; flag manifolds PDFBibTeX XMLCite \textit{F. Finster} and \textit{D. Schiefeneder}, Arch. Ration. Mech. Anal. 210, No. 2, 321--364 (2013; Zbl 1306.49060) Full Text: DOI arXiv References: [1] Bernard Y., Finster F.: On the structure of minimizers of causal variational principles in the non-compact and equivariant settings, arXiv:1205.0403 [math-ph]. Adv. Calc. Var. (2013, to appear) · Zbl 1281.49039 [2] Bröcker T., tom Dieck T.: Representations of compact Lie groups. In: Graduate Texts in Mathematics, vol. 98. 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