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On the Vector Sum of Two Convex Sets in Space

Published online by Cambridge University Press:  20 November 2018

Steven G. Krantz  and
Harold R. Parks
Steven G. Krantz
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences 1364 Budapest, P. O. Box 12 Hungary.
Harold R. Parks
Affiliation:
Department of Mathematics and Statistics McMaster University, HamiltonOntario L8S4K1.
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In the paper [KIS2], C. Kiselman studied the boundary smoothness of the vector sum of two smoothly bounded convex sets A and B in . He discovered the startling fact that even when A and B have real analytic boundary the set A + B need not have boundary smoothness exceeding C20/3 (this result is sharp). When A and B have C∞ boundaries, then the smoothness of the sum set breaks down at the level C5 (see [KIS2] for the various pathologies that arise).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 2 , 01 April 1991 , pp. 347 - 355
Copyright
Copyright © Canadian Mathematical Society 1991

References

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