Diffusion equation on curved surfaces. I. Theory and application to biological membranes

The effect of local curvature on the diffusion of a substance over a curved surface was discussed. These effects were characterized by the geodesic curvature kg(r) or by the Gaussian curvature K(r). The perturbations of the mean square geodesic distance traveled by a diffusing molecule on the surface and the probability distribution were presented as a function of the surface curvature. The correlations in the curvature were relevant to understand the lateral diffusion on biomembranes.