I wanted to know if there was some equivalent of Weyl law for the spectrum of the Jacobi operator of a minimal surface in the non-compact case. If the minimal surface is not closed, for example in $\mathbb{R}^3$, and $\varphi:\Sigma\rightarrow\mathbb{R}^3$ is a smooth minimal branched immersion from some surface $\Sigma$, and $M=\varphi(\Sigma)$ is a finite index minimal surface, the surface $\Sigma$ is not compact (and is actually conformally equivalent to a punctured RIemann surface), and classical Weyl's law seems to break out. Here if $g$ is the pull-back of the Euclidean metric on $\mathbb{R}^3$, then the Jacobi operator considered here is simply $\Delta_g-2K_g$, where $\Delta_g$ is the negative Lalace operator and $K_g$ is the Gauss curvature.