On the reconstruction of a star-shaped body from its “half-volumes”
- 1 October 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- Vol. 37 (2) , 243-257
- https://doi.org/10.1017/s1446788700022060
Abstract
The problem is the reconstruction of the shape of an object, whose shell is a surface star-shaped with respect to a point 0, from the knowledge of the volume of every “half-object” obtained by taking any plane through 0. Conditions for the existence and uniqueness of the solution are given. The main result consists in showing that any uniform a-priori bound on the mean curvature of the shell reestablishes continuous dependence on the data for bodies satisfying a certain symmetry condition.Keywords
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