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Improved Partial Regularity for Manifold-Constrained Minimisers of Subquadratic Energies

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Abstract

We consider minimising p-harmonic maps from three-dimensional domains to the real projective plane, for \(1<p<2\). These maps arise as least-energy configurations in variational models for nematic liquid crystals. We show that the singular set of such a map decomposes into a 1-dimensional set, which can be physically interpreted as a non-orientable line defect, and a locally finite set, i.e. a collection of point defects.

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Acknowledgements

We acknowledge the anonymous referees for their careful reading of the manuscript and for their suggestions, which improved the presentation of the results. G. C.’s research was supported by the Basque Government through the BERC 2018-2021 program and by the Spanish Ministry of Economy and Competitiveness: MTM2017-82184-R. G. O. was partially supported by GNAMPA-INdAM.

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  1. Dipartimento di Informatica, Università di Verona, Strada le Grazie 15, 37134, Verona, Italy

    Giacomo Canevari & Giandomenico Orlandi

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  1. Giacomo Canevari
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  2. Giandomenico Orlandi
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Correspondence to Giacomo Canevari.

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Communicated by H. T. Yau

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Canevari, G., Orlandi, G. Improved Partial Regularity for Manifold-Constrained Minimisers of Subquadratic Energies. Commun. Math. Phys. 374, 1483–1495 (2020). https://doi.org/10.1007/s00220-019-03675-2

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