Cartan-Hadamard 流形上的平移孤立子
微分几何
2023-04-03 v2
摘要
我们证明 Cartan-Hadamard 流形上平均曲率流的整体图 translator（即所谓 bowl soliton）的存在性结果。我们表明整体孤立子的渐近行为严重依赖于流形的曲率，并且若曲率足够快地趋于负无穷，也存在有界解。此外，在某些条件下甚至可解渐近 Dirichlet 问题。
引用
@article{arxiv.2007.02989,
title = {Translating solitons over Cartan-Hadamard manifolds},
author = {Jean-Baptiste Casteras and Esko Heinonen and Ilkka Holopainen and Jorge H. de Lira},
journal= {arXiv preprint arXiv:2007.02989},
year = {2023}
}
备注
This replaces the first version. We have deleted the whole Section 3 from the previous version due to a gap in a proof. We are grateful to Dr. Hengyu Zhou for pointing out the gap in the proof of Lemma 3.3 in the previous version