Translating solitons over Cartan-Hadamard manifolds
Differential Geometry
2023-04-03 v2
Abstract
We prove existence results for entire graphical translators of the mean curvature flow (the so-called bowl solitons) on Cartan-Hadamard manifolds. We show that the asymptotic behaviour of entire solitons depends heavily on the curvature of the manifold, and that there exist also bounded solutions if the curvature goes to minus infinity fast enough. Moreover, it is even possible to solve the asymptotic Dirichlet problem under certain conditions.
Keywords
Cite
@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}
}
Comments
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