Rectifiability of the singular set of multiple-valued energy minimizing harmonic maps
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- by Jonas Hirsch, Salvatore Stuvard and Daniele Valtorta PDF
- Trans. Amer. Math. Soc. 371 (2019), 4303-4352 Request permission
Abstract:
In this paper we study the singular set of energy minimizing $Q$-valued maps from $\mathbb {R}^m$ into a smooth compact manifold $\mathcal {N}$ without boundary. Similarly to what happens in the case of single valued minimizing harmonic maps, we show that this set is always $(m-3)$-rectifiable with uniform Minkowski bounds. Moreover, as opposed to the single-valued case, we prove that the target $\mathcal {N}$ being nonpositively curved but not simply connected does not imply continuity of the map.References
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Additional Information
- Jonas Hirsch
- Affiliation: Scuola Internazionale Superiore di Studi Avanzati, via Bonomea, 265, 34136 Trieste, Italy
- MR Author ID: 1179776
- Email: jonas.hirsch@sissa.it
- Salvatore Stuvard
- Affiliation: Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
- MR Author ID: 1231535
- ORCID: 0000-0002-3519-3653
- Email: salvatore.stuvard@math.uzh.ch
- Daniele Valtorta
- Affiliation: Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
- MR Author ID: 956785
- Email: daniele.valtorta@math.uzh.ch
- Received by editor(s): August 31, 2017
- Received by editor(s) in revised form: March 20, 2018
- Published electronically: November 2, 2018
- Additional Notes: The research of the first author has been supported by the MIUR SIR-grant “Geometric Variational Problems”, ID RBSI14RVEZ
The research of the second author was supported by the ERC-grant RAM “Regularity of Area Minimizing Currents”, ID 306246
The research of the third author has been supported by the SNSF grant PZ00P2_168006. - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 4303-4352
- MSC (2010): Primary 58E20; Secondary 49Q20
- DOI: https://doi.org/10.1090/tran/7595
- MathSciNet review: 3917224