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arXiv · 2204.11706

The X-ray transform on asymptotically conic spaces

András Vasy·Evangelie Zachos
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Abstract

In this paper, partly based on Zachos' PhD thesis, we show that the geodesic X-ray transform is stably invertible near infinity on a class of asymptotically conic manifolds which includes perturbations of Euclidean space. In particular certain kinds of conjugate points are allowed. Further, under a global convex foliation condition, the transform is globally invertible. The key analytic tool, beyond the approach introduced by Uhlmann and Vasy, is the introduction of a new pseudodifferential operator algebra, which we name the 1-cusp algebra, and its semiclassical version.

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András Vasy, Evangelie Zachos. 2022-04-25. The X-ray transform on asymptotically conic spaces. https://doi.org/10.2140/paa.2024.6.693

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