Infinite curvature on typical convex surfaces

Karim Adiprasito*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Solving a long-standing open question of Zamfirescu, we will show that typical convex surfaces contain points of infinite curvature in all tangent directions. To prove this, we use an easy curvature definition imitating the idea of Alexandrov spaces of bounded curvature, and show continuity properties for this notion.

Original languageAmerican English
Pages (from-to)267-275
Number of pages9
JournalGeometriae Dedicata
Issue number1
StatePublished - Aug 2012
Externally publishedYes

Bibliographical note

Funding Information:
The final preparation of this paper was supported by the DFG within the research training group “Methods for Discrete Structures” (GRK1408). It contains one of the results of the authors diploma thesis written at TU Dortmund, Germany.


  • Baire category
  • Convex body
  • Curvature
  • Typical
  • Umbilical points


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