The folding pattern of the human cortical surface is organized in a coherent set of troughs and ridges, which mark important anatomical demarcations that are similar across subjects. Cortical surface shape is often analyzed in the literature using isotropic diffusion, a strategy that is questionable because many anatomical regions are known to follow the direction of folds. This paper introduces anisotropic diffusion kernels to follow neighboring fold directions on surfaces, extending recent literature on enhancing curve-like patterns in images. A second contribution is to map deformations that affect sulcal length, i.e., are parallel to neighboring folds, with other deformations that affect sulcal length, within the diffusion process. Using the proposed method, we demonstrate anisotropic shape differences of the cortical surface associated with aging in a database of 95 healthy subjects, such as a contraction of the cingulate sulcus, shorter gyri in the temporal lobe and a contraction in the frontal lobe.