A framework for producing harmonic maps
arXiv:2607.14857
The paper develops a general method to generate families of harmonic maps from the unit ball to the Euclidean sphere, extending previous constructions and showing how these maps can solve various higher-order variational problems.
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, -harmonic maps as well as extrinsic polyharmonic maps.