Infinite curvature on typical convex surfaces
Metric Geometry
2011-09-13 v3 Differential Geometry
Abstract
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.
Cite
@article{arxiv.1011.4652,
title = {Infinite curvature on typical convex surfaces},
author = {Karim Adiprasito},
journal= {arXiv preprint arXiv:1011.4652},
year = {2011}
}
Comments
Pub version, to appear in Geometriae Dedicata