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More on compacta with convex projections
by
Stoyu Barov
The University of Alabama, Tuscaloosa
Coauthors: Jan Dijkstra (The University of Alabama)
The present research is in Geometric Tomography, which field deals with retrieval of information about an object in space from data concerning its shadows on planes. We obtain information about the structure of nonconvex compacta C (n >= 3) that have the property that every projection onto a hyperplane is convex. We find that if dimC <= n-2 then C contains n+1 copies of Sn-2 that are contained in distinct hyperplanes. If dimC >= n-1 then the existance of three and no more than three hyperplanes that intersect C in an (n-2)-sphere can be guaranteed.
Date received: February 9, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cady-39.