Abstract

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

Author information

Contact details are reproduced from the original publication and may be historical.

Karim Adiprasito

Institut für Mathematik, Freie Universität, Arnimallee 2, 14195 Berlin, Germany

karim.adip@web.de

Tudor Zamfirescu

Fakultät für Mathematik, Technische Universität, Vogelpothsweg 87, 44227 Dortmund, Germany
and: Institutul de Matematică al Academiei Române, Bucharest, Romania
and: School of Mathematical Sciences, GC University, Lahore, Pakistan

tuzamfirescu@gmail.com

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Suggested citation

K. Adiprasito, T. Zamfirescu. “Large Curvature on Typical Convex Surfaces.” Journal of Convex Analysis 19 (2012), No. 2, 385–391. https://doi.org/10.68381/jca19021

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Published by Heldermann Verlag, 2012. Rights now held by Banach Press LLC.