Search results for "Hadamard manifold"

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Translating Solitons Over Cartan-Hadamard Manifolds

2020

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.

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

2017

We study the geodesic X-ray transform on Cartan-Hadamard manifolds, and prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature decays at infinity. This work extends the results of Lehtonen (2016) to dimensions $n \geq 3$ and to the case of tensor fields of any order.

Mathematics - Differential GeometryPure mathematicsGeodesic01 natural sciencesTheoretical Computer ScienceTensor fieldHadamard transform44A12 53C21 53C22 45Q05Euclidean geometryFOS: MathematicsSectional curvatureTensor0101 mathematicsMathematical PhysicsMathematicsCartan-Hadamard manifoldsSolenoidal vector fieldApplied Mathematics010102 general mathematicsComputer Science Applications010101 applied mathematicsDifferential Geometry (math.DG)Bounded functionSignal Processingtensor tomographyMathematics::Differential GeometryInverse Problems
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