We show a Gromov-Hausdorff approximation to the product of the standard spheres $S^{n-p}\times S^p$ for Riemannian manifolds with positive Ricci curvature under some pinching condition on the eigenvalues of the Laplacian acting on functions and forms.
Ricci curvature and convergence of Lipschitz functions
A survey on the Convergence of Manifolds with Boundary
Ricci curvature and $L^p$-convergence
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