Explicit Estimates for the Bergman Kernel Form

Let $(L,e^{-ϕ})$ be a positive Hermitian holomorphic line bundle over a compact Riemann surface $X$, and let $ω=i\partial\overline\partialϕ$. We obtain explicit pointwise estimates for the Bergman form of the tensor power $mL$. If $\mathrm{Ric}ω\leqω$ and the shortest nonconstant closed geodesic has