Translating Solitons Over Cartan-Hadamard Manifolds
| Autor: | Jean-Baptiste Casteras, Esko Heinonen, Ilkka Holopainen, Jorge H. De Lira |
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| Přispěvatelé: | Department of Mathematics and Statistics, Geometric Analysis and Partial Differential Equations |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
Mathematics - Differential Geometry
Translating graphs mean curvature equation Translating solitons Riemannin monistot differentiaaligeometria Differential Geometry (math.DG) FOS: Mathematics 111 Mathematics Hadamard manifold Geometry and Topology Mathematics::Differential Geometry monistot translating graphs Cartan-Hadamard manifold 53C21 53C44 |
| Popis: | 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. Comment: 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 |
| Databáze: | OpenAIRE |
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