Regularity of harmonic maps from polyhedra to CAT(1) spaces

We determine regularity results for energy minimizing maps from an n -dimensional Riemannian polyhedral complex X into a CAT(1) space. Provided that the metric on X is Lipschitz regular, we prove Hölder regularity with Hölder constant and exponent dependent on the total energy of the map and the met...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2018-02, Vol.57 (1), p.1-35, Article 12
Main Authors: Breiner, Christine, Fraser, Ailana, Huang, Lan-Hsuan, Mese, Chikako, Sargent, Pam, Zhang, Yingying
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Combinatorial analysis
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Regularity
Systems Theory
Theoretical
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Summary:We determine regularity results for energy minimizing maps from an n -dimensional Riemannian polyhedral complex X into a CAT(1) space. Provided that the metric on X is Lipschitz regular, we prove Hölder regularity with Hölder constant and exponent dependent on the total energy of the map and the metric on the domain. Moreover, at points away from the ( n - 2 ) -skeleton, we improve the regularity to locally Lipschitz. Finally, for points x ∈ X ( k ) with k ≤ n - 2 , we demonstrate that the Hölder exponent depends on geometric and combinatorial data of the link of x ∈ X .
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-017-1279-5