3 problems

Let $T_m$ be the modular punctured torus, let $A_m=1.08...$ be the area of its associated unit ball, and let $N_L(T_m)$ denote the number of geodesic loops of length at most $L$ on…

Let $T$ be a hyperbolic punctured torus, let ${\cal B}_\ell(T)$ be its associated unit ball, and let $T_m=\Gamma\backslash {\bf H}^2$ be the modular punctured torus, where $\Gamma$…

Let ${\mathcal L}_c$ denote the linear slice at parameter $c$, and distinguish its standard component from its non-standard components. Critical-length conjecture. There exists a u…