Systole growth for finite area hyperbolic surfaces

Florent Balacheff; Eran Makover; Hugo Parlier

Systole growth for finite area hyperbolic surfaces

Geometric Topology 2014-10-02 v2 Differential Geometry

Authors: Florent Balacheff , Eran Makover , Hugo Parlier

Abstract

We are interested in the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature $(g,n)$ . This maximum is shown to be strictly increasing in terms of the number of cusps for small values of $n$ . We also show that this function is greater than a function that grows logarithmically in function of the ratio $g/n$ .

Keywords

systole hyperbolic surfaces finite area cusps signature growth rate

Cite

@article{arxiv.1201.3468,
  title  = {Systole growth for finite area hyperbolic surfaces},
  author = {Florent Balacheff and Eran Makover and Hugo Parlier},
  journal= {arXiv preprint arXiv:1201.3468},
  year   = {2014}
}

Comments

8 pages, 1 figure. Removed Part 3 of main theorem due to an error in Lemma 3

Systole growth for finite area hyperbolic surfaces

Abstract

Keywords

Cite

Comments

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