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 |
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Pages (from-to) | 267-275 |
Number of pages | 9 |
Journal | Geometriae Dedicata |
Volume | 159 |
Issue number | 1 |
DOIs | |
State | Published - Aug 2012 |
Externally published | Yes |
Bibliographical 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.
Keywords
- Baire category
- Convex body
- Curvature
- Typical
- Umbilical points