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arXiv · 1507.06355

Growth of Hyperbolic Cells

Pritha Chakraborty
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Abstract

We consider a hyperbolic polygon in the unit disk $\{z:\, |z|<1\}$ with all its vertices on the unit circle $\{z:\, |z|=1\}$ and a growth process of such polygons when each $n$-gon generates an $n(n-1)$-gon by inverting itself across all of its sides. In this paper, we prove some general monotonicity results of inversion for convex hyperbolic $n$-gons and solve an extremal problem that, among all convex hyperbolic $4$-gons containing the origin, the inverted side length of the longest side of the given hyperbolic $4$-gon is minimal for the regular hyperbolic $4$-gon.

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Pritha Chakraborty. 2015-07-22. Growth of Hyperbolic Cells. https://arxiv.org/abs/1507.06355

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