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

The support of minimizing measures of the causal variational principle on the sphere is analyzed. It is proven that in the case τ > 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 τ >...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations Vol. 58; no. 6; pp. 1 - 27
Main Authors: Bäuml, Lucia, Finster, Felix, Schiefeneder, Daniela, von der Mosel, Heiko
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2019
Springer Nature B.V
Subjects:
Analysis
Calculus of Variations and Optimal Control; Optimization
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
58Z05
49S05
49N60
49Q20
28C99
58C35
ISSN:0944-2669, 1432-0835
Online Access:Get full text
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Summary:The support of minimizing measures of the causal variational principle on the sphere is analyzed. It is proven that in the case τ > 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 τ > 6 , the support is proven to have Hausdorff dimension at most 6 / 7.
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content type line 14
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-019-1652-7