Holographic entanglement entropy from minimal surfaces with/without extrinsic curvature

In this paper we show that in addition to the known minimal surfaces which appear in the literature for computing the holographic entanglement entropy, there are other minimal surfaces with non-zero extrinsic curvature. we use the approach of regularization procedure presented by fursaev et al. in [7], to compute the quadratic and cubic curvature invariants on manifolds with squashed cones. the results can be used to find the leading and universal terms of the holographic entanglement entropy to understand which solution corresponds to the actual minimal entropy.