Curvature-induced melting-temperature depression ($T_I=T_m-\gamma T_m\mathcal{K}/(\rho L)$)

Curvature depresses the equilibrium melting temperature of solid convex into liquid. Here $\mathcal{K}$ is the sum of principal curvatures, equal to twice a common convention for mean curvature, and $T_m$ is absolute temperature. The coefficient uses solid-liquid surface energy, mass density and latent heat. This stabilizes fine corrugations of a solidification front.