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Transactions of the American Mathematical Society

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

 

 

Bonnesen-style inequalities for Minkowski relative geometry


Author: J. R. Sangwine-Yager
Journal: Trans. Amer. Math. Soc. 307 (1988), 373-382
MSC: Primary 52A40; Secondary 52A20
DOI: https://doi.org/10.1090/S0002-9947-1988-0936821-5
MathSciNet review: 936821
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Abstract: Two Bonnesen-style inequalities are obtained for the relative inradius of one convex body with respect to another in $ n$-dimensional space. Both reduce to the known planar inequality; one sharpens the relative isoperimetric inequality, the other states that a quadratic polynomial is negative at the inradius. Circumradius inequalities follow.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0936821-5
Keywords: Circumradius, convex body, inner parallel body, inradius, quermassintegral
Article copyright: © Copyright 1988 American Mathematical Society