$\mathbb{R}^3$ 与 $\mathbb{R}^4$ 中的 H-流平移孤立子
微分几何
2012-05-22 v3 偏微分方程分析
摘要
受 Ilmanen 对应的启发，我们针对欧氏 4 维空间中平均曲率流的非极小平移子，给出了 prescribed Hoffman-Osserman Gauss map 问题的显式解。我们提出了关于 Jenkins-Serrin 型单位速度图平移子不存在性的猜想。
引用
@article{arxiv.1204.0243,
title = {The H-flow translating solitons in R^3 and R^4},
author = {Hojoo Lee},
journal= {arXiv preprint arXiv:1204.0243},
year = {2012}
}
备注
Example 3 and an acknowledgement are added. As an application of our prescribed Gauss map representation of translators in R^4, we explicitly determine the Hoffman-Osserman Gauss map of the Hamiltonian stationary Lagrangian translator in C^2