Mathematical Sciences: RUI: Geometric Tomography

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Gardner 9501289 The proposed research is in the area of geometric tomography and convexity theory. The proposer wishes to extend his earlier work on the Busemann-Petty problem dealing with convex bodies: the Busemann-Petty problem has to do with drawing conclusions about the relative volumes of two convex bodies in n-space from information about their central sections. The X-ray problem - reconstruction of a convex body from a small number of X-ray pictures - is considered; the proposed research has potentially significant ramifications in computerized tomography (CAT and MRI scanners).