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arXiv · 1311.3947

On maximally inflected hyperbolic curves

Aubin Arroyo·Erwan Brugallé·Lucia López de Medrano
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Abstract

In this note we study the distribution of real inflection points among the ovals of a real non-singular hyperbolic curve of even degree. Using Hilbert's method we show that for any integers $d$ and $r$ such that $4\leq r \leq 2d^2-2d$, there is a non-singular hyperbolic curve of degree $2d$ in $\mathbb R^2$ with exactly $r$ line segments in the boundary of its convex hull. We also give a complete classification of possible distributions of inflection points among the ovals of a maximally inflected non-singular hyperbolic curve of degree $6$.

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Aubin Arroyo, Erwan Brugallé, Lucia López de Medrano. 2013-11-15. On maximally inflected hyperbolic curves. https://arxiv.org/abs/1311.3947

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