On Halpern’s conjecture for closed plane curves
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- by Tetsuya Ozawa PDF
- Proc. Amer. Math. Soc. 92 (1984), 554-560 Request permission
Abstract:
Let $c$ be a smooth closed plane curve given in general position. A bitangent of $c$ is, by definition, a line which is tangent to $c$ at two different points. Let $B(c)$ and $D(c)$ denote the numbers of all bitangents and all double points of $c$, respectively. We prove here that if $c$ has no inflection points, $B(c) \leqslant D(c)(2D(c) - 1)$. This is the affirmative answer to Halpern’s conjecture.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 554-560
- MSC: Primary 53A04; Secondary 52A10
- DOI: https://doi.org/10.1090/S0002-9939-1984-0760945-0
- MathSciNet review: 760945