Stability results for sections of convex bodies

M. Stephen, V. Yaskin

Research output: Contribution to journalArticlepeer-review


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 Koldob-sky and Shane about determination of convex bodies by fractional derivatives of the parallel section function and establish the corresponding stability result.

Original languageEnglish
Pages (from-to)6239-6261
Number of pages23
JournalTransactions of the American Mathematical Society
Issue number9
StatePublished - 2017
Externally publishedYes


  • Cross-section body
  • Intersection body
  • Stability


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