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arXiv · 2107.03715

On the equivariant stability of harmonic self-maps of cohomogeneity one manifolds

Volker Branding·Anna Siffert
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Abstract

The systematic study of harmonic self-maps on cohomogeneity one manifolds has recently been initiated by P\"uttmann and the second named author in \cite{MR4000241}. In this article we investigate the corresponding Jacobi equation describing the equivariant stability of such harmonic self-maps. Besides several general statements concerning their equivariant stability we explicitly solve the Jacobi equation for some harmonic self-maps in the cases of spheres, special orthogonal groups and $\SU(3)$. In particular, we show by an explicit calculation that for specific cohomogeneity one actions on the sphere the identity map is equivariantly stable.

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Volker Branding, Anna Siffert. 2021-07-08. On the equivariant stability of harmonic self-maps of cohomogeneity one manifolds. https://doi.org/10.1016/j.jmaa.2022.126635

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