Minimal hypersurfaces in manifolds of Ricci curvature bounded below (Q2082109)

In this paper, the author studies the angle estimate of distance functions from minimal hypersurfaces in manifolds of Ricci curvature bounded from below, using Colding's method developed in [\textit{T. H. Colding}, Ann. Math. (2) 145, No. 3, 477--501 (1997; Zbl 0879.53030)]. Using the Cheeger-Colding theory, the author obtains the Laplacian comparison for limits of distance functions from minimal hypersurfaces in the version of Ricci limit space. The results obtained are applied to show that, 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 cone \(CX \times {\mathbb R}^{n-k}\) obtained from ambient manifolds of almost nonnegative Ricci curvature, then a Frankel property for the cross section \(Y\) of \(CY\) holds, namely \(Y\) has only connected component in \(X\).