A1 Journal article (refereed)
Translating Solitons Over Cartan–Hadamard Manifolds (2023)

Casteras, J.-B., Heinonen, E., Holopainen, I., & De Lira, J. H. (2023). Translating Solitons Over Cartan–Hadamard Manifolds. Journal of Geometric Analysis, 33(5), Article 163. https://doi.org/10.1007/s12220-023-01218-9

JYU authors or editors

Publication details

All authors or editors: Casteras, Jean-Baptiste; Heinonen, Esko; Holopainen, Ilkka; De Lira, Jorge H.

Journal or series: Journal of Geometric Analysis

ISSN: 1050-6926

eISSN: 1559-002X

Publication year: 2023

Publication date: 28/02/2023

Volume: 33

Issue number: 5

Article number: 163

Publisher: Springer Science and Business Media LLC

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1007/s12220-023-01218-9

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/85910

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2007.02989

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 behavior 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: differential geometry; manifolds (mathematics); Riemannian manifolds

Free keywords: mean curvature equation; translating graphs; Hadamard manifold

Contributing organizations

Ministry reporting: Yes

VIRTA submission year: 2023

JUFO rating: 2