Stability results for sections of convex bodies

Stephen, M.; Yaskin, V.

doi:10.1090/tran/6854

Stability results for sections of convex bodies
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by M. Stephen and V. Yaskin PDF

Trans. Amer. Math. Soc. 369 (2017), 6239-6261 Request permission

Abstract:

It is shown by Makai, Martini, and Ódor that a convex body $K$, all of whose maximal sections pass through the origin, must be origin-symmetric. We prove a stability version of this result. We also discuss a theorem of Koldobsky and Shane about determination of convex bodies by fractional derivatives of the parallel section function and establish the corresponding stability result.

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