Large curvature on typical convex surfaces

Karim Adiprasito, Tudor Zamfirescu

Research output: Contribution to journalArticlepeer-review


We show in this paper that on most convex surfaces there exist points with arbitrarily large lower curvature in every tangent direction. Moreover, we show that, astonishingly, on most convex surfaces, although the set of points with curvature 0 in every tangent direction has full measure, it contains no pair of opposite points, i.e. points admitting parallel supporting planes.

Original languageAmerican English
Pages (from-to)385-391
Number of pages7
JournalJournal of Convex Analysis
Issue number2
StatePublished - 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • General Mathematics


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