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Misha
Misha
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For Question 2: In addition to Kellerhals' lower bounds on $\epsilon(n)$, there existsis an absolute constant $C>0$ such that $$ \epsilon(n)\le \frac{C}{\sqrt{n}}, $$ see Proposition 5.2 in

Belolipetsky, Mikhail, Proposition 5.2 hereHyperbolic orbifolds of small volume, Jang, Sun Young (ed.) et al., Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13–21, 2014. Vol. II: Invited lectures. Seoul: KM Kyung Moon Sa (ISBN 978-89-6105-805-6/hbk; 978-89-6105-803-2/set). 837-851 (2014). ZBL1373.22017.

The paper is also available in arXiv here.

For Question 2: In addition to Kellerhals' lower bounds on $\epsilon(n)$, there exists an absolute constant $C>0$ such that $$ \epsilon(n)\le \frac{C}{\sqrt{n}}, $$ see Proposition 5.2 here.

For Question 2: In addition to Kellerhals' lower bounds on $\epsilon(n)$, there is an absolute constant $C>0$ such that $$ \epsilon(n)\le \frac{C}{\sqrt{n}}, $$ see Proposition 5.2 in

Belolipetsky, Mikhail, Hyperbolic orbifolds of small volume, Jang, Sun Young (ed.) et al., Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13–21, 2014. Vol. II: Invited lectures. Seoul: KM Kyung Moon Sa (ISBN 978-89-6105-805-6/hbk; 978-89-6105-803-2/set). 837-851 (2014). ZBL1373.22017.

The paper is also available in arXiv here.

Source Link
Misha
Misha
  • 31.2k
  • 1
  • 94
  • 163

For Question 2: In addition to Kellerhals' lower bounds on $\epsilon(n)$, there exists an absolute constant $C>0$ such that $$ \epsilon(n)\le \frac{C}{\sqrt{n}}, $$ see Proposition 5.2 here.