AI 中文总结
该研究提出从单位球到欧几里得球面生成调和映射族的框架，基于托特工作，为广义径向投影提供理论背景，还指出这些映射族可用于构建相关变分问题的解。
AI 中文摘要
我们提出了一个通用框架，用于从单位球到欧几里得球面生成调和映射族，起始于一个固定的调和映射。特别地，我们的分析为中内最近引入的广义径向投影提供了理论背景。我们的方法基于托特的工作，他建立了一种从给定特征映射生成球之间特征映射的机制。最后，我们指出这些调和映射族可用于构建相关变分问题的解，如内在双调和和三调和映射、p - 调和映射以及外在多调和映射。
英文摘要
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.
