Convergence to the Product of the Standard Spheres and Eigenvalues of the Laplacian

Abstract

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.

References in corpus (2)

• Local Poincaré inequalities from stable curvature conditions on metric spaces
• Recognizing the flat torus among $RC{D}^{\ast }(0,N)$ spaces via the study of the first cohomology group