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3
votes
Packing and isoperimetrics
László Fejes Tóth considered the planar version in his book Regular Figures. On page 175, he gives the following theorem, which verifies your guess (discs here does not necessarily mean circular discs …
13
votes
Accepted
General Isoperimetric Inequality via Representation Theory of SO(n)
For the second time today (see Bodies of constant width?), I give the answer: see "Geometric Applications of Fourier Series and Spherical Harmonics" by Helmut Groemer. That book deals exactly with you …
4
votes
1
answer
682
views
Generalized widths and reverse Urysohn inequalities
This question is inspired by the discussion in MO questions "Local minimum from directional derivatives in the space of convex bodies" and "Bodies of constant width?" about generalized notions of min …