In this paper, we study the angle estimate of distance functions from minimal hypersurfaces in manifolds of Ricci curvature bounded from below using Colding's method in [13]. With Cheeger-Colding theory, we obtain the Laplacian comparison for limits of distance functions from minimal hypersurfaces in the version of Ricci limit space. As an application, if a sequence of minimal hypersurfaces converges to a metric cone $CY\times\mathbb{ R}^{ n-k}(2\leq k\leq n)$ in a non-collapsing metric cone $CX\times\mathbb{ R}^{ n-k}$ obtained from ambient manifolds of almost nonnegative Ricci curvature, then we can prove a Frankel property for the cross section $Y$ of $CY$. Namely, $Y$ has only one connected component in $X$.
Categories: math.DG