Geometriae Dedicata

, Volume 159, Issue 1, pp 267–275 | Cite as

Infinite curvature on typical convex surfaces

  • Karim Adiprasito


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.


Baire category Convex body Typical Curvature Umbilical points 

Mathematics Subject Classification (2000)

52A20 52A23 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Freie Universität BerlinBerlinGermany

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