Collapsing and the Differential Form Laplacian : The Case of a Smooth Limit Space

1999/02/18 by John Lott, Lott, John
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.math/9902111

Final version of the case of a smooth limit space. The case of a singular limit space will appear separately

openalex publication_date 1999/02/18 · arxiv created 2001/09/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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