Equivariant harmonic maps depend real analytically on the representation

Slegers, Ivo

doi:10.1007/s00229-021-01345-z

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Equivariant harmonic maps depend real analytically on the representation

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Slegers, Ivo
Max Planck Institute for Mathematics, Max Planck Society;

Externe Ressourcen

https://doi.org/10.1007/s00229-021-01345-z
(Verlagsversion)

https://doi.org/10.48550/arXiv.2007.14291
(Preprint)

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Slegers_Equivariant harmonic maps depend real analytically on the representation_2022.pdf
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Slegers, I. (2022). Equivariant harmonic maps depend real analytically on the representation. Manuscripta mathematica, 169(3-4), 633-648. doi:10.1007/s00229-021-01345-z.

Zitierlink: https://hdl.handle.net/21.11116/0000-0009-7799-5

Zusammenfassung

We consider harmonic maps into symmetric spaces of non-compact type that are equivariant for representations that induce a free and proper action on the symmetric space. We show that under suitable non-degeneracy conditions such equivariant harmonic maps depend in a real analytic fashion on the representation they are associated to. The main tool in the proof is the construction of a family of deformation maps which are used to transform equivariant harmonic maps into maps mapping into a fixed target space so that a real analytic version of the results in [4] can be applied.