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1. An extremal property of the symmetric decreasing rearrangement

Author

Hoehner, Steven and Novaes, Júlia

Subjects
Mathematics - Functional Analysis, Mathematics - Metric Geometry, 39B62 (Primary) 52A20, 52A40, 52A41 (Secondary)
Abstract

Let $\alpha$ be a given real number. It is shown that for a given $\alpha$-concave function, its symmetric decreasing rearrangement is always harder to approximate in the symmetric difference metric by $\alpha$-affine minorants with a fixed number of break points. This extends a classical result of Macbeath (1951) from convex bodies to a functional setting., Comment: 11 pages, 1 figure

Published
2023

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