Systole growth for finite area hyperbolic surfaces

Florent Balacheff; Eran Makover; Hugo Parlier

Annales de la faculté des sciences de Toulouse Mathématiques (2014)

  • Volume: 23, Issue: 1, page 175-180
  • ISSN: 0240-2963

Abstract

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In this note, we observe that the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature ( g , n ) is greater than a function that grows logarithmically in terms of the ratio g / n .

How to cite

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Balacheff, Florent, Makover, Eran, and Parlier, Hugo. "Systole growth for finite area hyperbolic surfaces." Annales de la faculté des sciences de Toulouse Mathématiques 23.1 (2014): 175-180. <http://eudml.org/doc/275308>.

@article{Balacheff2014,
abstract = {In this note, we observe that the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature $(g,n)$ is greater than a function that grows logarithmically in terms of the ratio $g/n$.},
author = {Balacheff, Florent, Makover, Eran, Parlier, Hugo},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Rieman surface; systole function},
language = {eng},
number = {1},
pages = {175-180},
publisher = {Université Paul Sabatier, Toulouse},
title = {Systole growth for finite area hyperbolic surfaces},
url = {http://eudml.org/doc/275308},
volume = {23},
year = {2014},
}

TY - JOUR
AU - Balacheff, Florent
AU - Makover, Eran
AU - Parlier, Hugo
TI - Systole growth for finite area hyperbolic surfaces
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2014
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 1
SP - 175
EP - 180
AB - In this note, we observe that the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature $(g,n)$ is greater than a function that grows logarithmically in terms of the ratio $g/n$.
LA - eng
KW - Rieman surface; systole function
UR - http://eudml.org/doc/275308
ER -

References

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  2. Beardon (A.), Minda (D.).— The hyperbolic metric and geometric function theory. Quasiconformal mappings and their applications, p. 9-56, Narosa, New Delhi (2007). Zbl1208.30001MR2492498
  3. Buser (P.), Sarnak (P.).— On the period matrix of a Riemann surface of large genus. With an appendix by J. H. Conway and N. J. A. Sloane. Invent. Math. 117, no. 1, p. 27-56 (1994). Zbl0814.14033MR1269424
  4. Farb (B.), Margalit (D.).— A primer on mapping class groups. To appear in Princeton Mathematical Series. Zbl1245.57002MR2850125
  5. Mumford (D.).— A remark on a Mahler’s compactness theorem. Proc. AMS 28, no. 1, p. 289-294 (1971). Zbl0215.23202MR276410
  6. Schmutz (P.).— Congruence subgroups and maximal Riemann surfaces. J. Geom. Anal. 4, p. 207-218 (1994). Zbl0804.32010MR1277506

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