Infinite curvature on typical convex surfaces

Details Infinite curvature on typical convex surfaces Infinite curvature on typical convex surfaces

2010-11-21

arxiv.org/abs/1011.4652v3

Mathematics

Metric Geometry

Pub version, to appear in Geometriae Dedicata

Scientific paper

Solving a long-standing open question in convex geometry, 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. Along the way, we show a theorem for the approximation of convex surfaces by smooth surfaces.

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