On Hadwiger’s results concerning Minkowski sums and isoperimetric inequalities for moments of inertia
نویسنده
چکیده
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.
منابع مشابه
Minkowski sums and isoperimetric inequalities for polar moments of inertia of plane convex regions
These notes are to be regarded as a ‘plea for help’. Although I continue to make progress at proofs, the progress is slow. I am out of my usual area of work, and others, more expert in convex geometry matters, may well be able to tell me whether things that I’m trying to prove are true or not, or unknown. My email is [email protected] Assistance with settling the questions associated with ...
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