2 problems

Let $\Sigma$ be a compact surface with singular points $p_1,\ldots,p_m$ and ordered weights $-1<\alpha_1\leq\cdots\leq\alpha_m<0$. For $\rho>0$, let…

Let $\Sigma$ be a compact surface with singular points $p_1,\ldots,p_m$ and weights $-1<\alpha_1\leq\cdots\leq\alpha_m<0$. For $\rho>0$, let $\Sigma_{\rho,\underline{\alpha}}$ deno…