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Support theorem for the Light-Ray transform of vector fields on Minkowski spaces

Partly supported by NSF Grants DMS 1301646 and DMS 1600327.

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  • We study the Light-Ray transform of integrating vector fields on the Minkowski time-space $\boldsymbol{{\rm R}}^{1+n}$, $n≥ 2$, with the Minkowski metric. We prove a support theorem for vector fields vanishing on an open set of light-like lines. We provide examples to illustrate the application of our results to the inverse problem for the hyperbolic Dirichlet-to-Neumann map.

    Mathematics Subject Classification: 44A12, 46F12, 53C65.


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  • Figure 1.  $\Gamma_{\rho_0}$ with $0 <c < 1$.

    Figure 2.  $\Gamma_{0}$ with $0 <c <1$.

    Figure 3.  $\Gamma_{0}$ with $0 <c < 1$.

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