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

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

1999-02-18

arxiv.org/abs/math/9902111v5

Mathematics

Differential Geometry

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

Scientific paper

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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