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Collapsing and the differential form Laplacian: the case of a smooth limit space. (English) Zbl 1072.58023

Author’s abstract: We analyze the limit of the \(p\)-form Laplacian under a collapse, with bounded sectional curvature and bounded diameter, to a smooth limit space. As an application, we characterize when the \(p\)-form Laplacian has small positive eigenvalues in a collapsing sequence.

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
35P15 Estimates of eigenvalues in context of PDEs
31C12 Potential theory on Riemannian manifolds and other spaces
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