Relating Symmetrizations of Convex Bodies: Once More the Golden Ratio

@article{Brandenberg2022RelatingSO,
  title={Relating Symmetrizations of Convex Bodies: Once More the Golden Ratio},
  author={Ren{\'e} Brandenberg and Katherina von Dichter and Bernardo Gonz{\'a}lez Merino},
  journal={The American Mathematical Monthly},
  year={2022},
  volume={129},
  pages={352 - 362}
}
Abstract Similar to the arithmetic-harmonic mean inequality for numbers, the harmonic mean of two convex sets K and C is always contained in their arithmetic mean. The harmonic and arithmetic means of C and – C define two different symmetrizations of C, each keeping some useful properties of the original set. We investigate the relations of such symmetrizations, involving a suitable measure of asymmetry—the Minkowski asymmetry, which, besides other advantages, is polynomial time computable for… 
1 Citations
Tightening and reversing the arithmetic-harmonic mean inequality for symmetrizations of convex sets
This paper deals with four symmetrizations of a convex set C: the intersection, the harmonic and the arithmetic mean, and the convex hull of C and −C. A well-known result of Firey shows that those

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