Measured Hausdorff convergence of Riemannian manifolds and Laplace operators (Q1327617)

The author studies the Laplace operators of Riemannian manifolds which collapse to a space of lower dimension while their curvature stays bounded. \textit{K. Fukaya} [Invent. Math. 87, 517-547 (1987; Zbl 0589.58034)]\ has discussed the continuity of eigenvalues of Laplace operators with uniformly bounded curvature with respect to the measured Hausdorff topology on the set of metric spaces equipped with Borel measures. The present paper contains a detailed statement of the relationship of the Laplace operator \(\Delta_i\) of \(M_i\) and the operator \({\mathcal L}_\infty\) on the limit manifold \(M_\infty\).