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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Adjoint transform, overconvexity and sets of constant width


Author: François Bavaud
Journal: Trans. Amer. Math. Soc. 333 (1992), 315-324
MSC: Primary 52A10; Secondary 52A22
DOI: https://doi.org/10.1090/S0002-9947-1992-1132431-9
MathSciNet review: 1132431
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Abstract: The properties of the adjoint transform (associating to a set the intersection of all disks of given radius centered in the set) are systematically investigated, in particular its relationship with the overconvex, the parallelisation and completion of sets. Sets conjugate by the transform can be characterised in a new way as the union or the intersection of all completions of the reference body. New relationships satisfied by their areas and perimeters are derived. Two applications in problems of random intersection of disks are finally treated.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1132431-9
Article copyright: © Copyright 1992 American Mathematical Society

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