  In the context of the surface-state correspondence we propose the geodesic
curvature of a convex curve as a local measure of factorization of the dual CFT
state. Its integral will be interpreted as computing the bipartite entanglement
among degrees of freedom with support on the chosen domain. We will derive
results through application of the Gauss-Bonnet theorem and show quantitative
agreement with computations using the MERA tensor network and the formalism of
entanglement density.
