Tensor Tomography on Negatively Curved Manifolds of Low Regularity
Ilmavirta, J., & Kykkänen, A. (2024). Tensor Tomography on Negatively Curved Manifolds of Low Regularity. Journal of Geometric Analysis, 34, Article 147. https://doi.org/10.1007/s12220-024-01588-8
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Journal of Geometric AnalysisDate
2024Copyright
© The Author(s) 2024
We prove solenoidal injectivity for the geodesic X-ray transform of tensor fields on simple Riemannian manifolds with C1,1 metrics and non-positive sectional curvature. The proof of the result rests on Pestov energy estimates for a transport equation on the non-smooth unit sphere bundle of the manifold. Our low regularity setting requires keeping track of regularity and making use of many functions on the sphere bundle having more vertical than horizontal regularity. Some of the methods, such as boundary determination up to gauge and regularity estimates for the integral function, have to be changed substantially from the smooth proof. The natural differential operators such as covariant derivatives are not smooth.
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https://converis.jyu.fi/converis/portal/detail/Publication/207816543
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Research Council of FinlandFunding program(s)
Academy Research Fellow, AoF; Others, AoF; Centre of Excellence, AoF; Research costs of Academy Research Fellow, AoFAdditional information about funding
Both authors we supported by the Academy of Finland (JI by grant 351665, AK by grant 351656). AK was supported by the Finnish Academy of Science and Letters. This work was supported by the Research Council of Finland (Flagship of Advanced Mathematics for Sensing Imaging and Modelling grant 359208 and Centre of Excellence of Inverse Modelling and Imaging 353092). Open Access funding provided by University of Jyväskylä (JYU). ...License
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