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arXiv · 2305.10501

An extremal property of the symmetric decreasing rearrangement

Steven Hoehner·Júlia Novaes
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Abstract

It is shown that for a given log-concave function, its symmetric decreasing rearrangement is always harder to approximate in the symmetric difference metric by inner log-linearizations with a fixed number of break points. This extends a classical result of Macbeath (1951) from convex bodies to a functional setting.

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Steven Hoehner, Júlia Novaes. 2023-05-17. An extremal property of the symmetric decreasing rearrangement. https://arxiv.org/abs/2305.10501

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