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On the reconstruction of a star-shaped body from its “half-volumes”

Part of: Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Stefano Campi
Stefano Campi
Affiliation:
Istituto Matematico “U. Dini”Viale Morgagni 67/A Firenze, Italy
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Abstract

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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.

MSC classification

Secondary: 53C65: Integral geometry
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 2 , October 1984 , pp. 243 - 257
Copyright
Copyright © Australian Mathematical Society 1984

References

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