A Support Theorem for the Geodesic Ray Transform on Functions

By Venkateswaran P. Krishnan. 2007

59 citations recorded by the source corpus.

Let (M,g) be a simple Riemannian manifold. Under the assumption that the metric g is real-analytic, it is shown that if the geodesic ray transform of a function f∈L2(M) vanishes on an appropriate open set of geodesics, then f=0 on the set of points lying on these geodesics. The approach is based on analytic microlocal analysis.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/31f1871360f890ec5979f6cbd704cb67fb346a58

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In Applied Mathematics

1. Gunther Uhlmann
2. Mikko Salo
3. Carlos E. Kenig
4. András Vasy
5. David dos Santos Ferreira
6. Aynur Bulut
7. C. Guillarmou
8. Raphael Cote

In Astronomy and Astrophysics

1. Mikko Salo
2. Gunther Uhlmann
3. András Vasy
4. Carlos E. Kenig
5. Plamen Stefanov

In Mathematical Physics

1. Gunther Uhlmann
2. Mikko Salo
3. Carlos E. Kenig
4. András Vasy
5. David dos Santos Ferreira
6. Matti Lassas
7. Katya Krupchyk
8. Yi-Hsuan Lin

Citations in the corpus

• The inverse problem for the local geodesic ray transform (2012, result): “Our results generalize support type theorems to the smooth case for the geodesic X-ray transform given in [8] for simple real-analytic metrics.”
• The Calderón problem with partial data on manifolds and applications (2012, background): “2 and [Krishnan 2009] imply, as in Section 3A, that”