Infinite curvature on typical convex surfaces

Karim Adiprasito

doi:10.1007/s10711-011-9658-0

Infinite curvature on typical convex surfaces

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	267-275
Number of pages	9
Journal	Geometriae Dedicata
Volume	159
Issue number	1
DOIs	https://doi.org/10.1007/s10711-011-9658-0
State	Published - Aug 2012
Externally published	Yes

Keywords

Baire category
Convex body
Curvature
Typical
Umbilical points

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1007/s10711-011-9658-0

Cite this

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author = "Karim Adiprasito",

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.",

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KW - Umbilical points

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Infinite curvature on typical convex surfaces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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