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RESEARCH PRODUCT

Translating Solitons Over Cartan-Hadamard Manifolds

Jean-baptiste CasterasEsko HeinonenIlkka HolopainenJorge H. De Lira

subject

Mathematics - Differential GeometryTranslating graphsmean curvature equationTranslating solitonsRiemannin monistotdifferentiaaligeometriaDifferential Geometry (math.DG)FOS: Mathematics111 MathematicsHadamard manifoldGeometry and TopologyMathematics::Differential Geometrymonistottranslating graphsCartan-Hadamard manifold53C21 53C44

description

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.

yearjournalcountryeditionlanguage
2020-07-06
10.1007/s12220-023-01218-9http://hdl.handle.net/10138/356706