On Hadwiger's Results Concerning Minkowski Sums and Isoperimetric Inequalities for Moments of Inertia

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Keady, Grant (2006) On Hadwiger's Results Concerning Minkowski Sums and Isoperimetric Inequalities for Moments of Inertia. Research report collection, 9 (4).

Abstract

Consider convex plane domains D(t) = (1−t)D₀ + tD₁, 0 ≤ t ≤ 1. We first prove that the 1/4-power of the polar moment of inertia about the centroid of D(t) is concave in t. From this we deduce some isoperimetric inequalities.

Item type Article
URI https://vuir.vu.edu.au/id/eprint/17583
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords moment of domain, Brunn-Minkowski, Prekopa-Leindler, isoperimetric inequality
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