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arXiv · 2607.14857

A framework for producing harmonic maps

Volker Branding·Anna Siffert
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Abstract

We present a general framework for producing families of harmonic maps from the unit ball into the Euclidean sphere starting from a fixed harmonic map. In particular, our analysis provides a theoretical background for a generalized radial projection which was recently introduced by Nakauchi. Our approach is based on work of Toth who established a machinery that generates eigenmaps between spheres from a given eigenmap. Finally, we point out how these families of harmonic maps can be used to construct solutions to associated variational problems such as intrinsic biharmonic and triharmonic maps, $p$-harmonic maps as well as extrinsic polyharmonic maps.

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Volker Branding, Anna Siffert. 2026-07-16. A framework for producing harmonic maps. https://arxiv.org/abs/2607.14857

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