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arXiv · 1705.08400

Eigenvalue estimates and differential form Laplacians on Alexandrov spaces

John Lott
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Abstract

We give upper bounds on the eigenvalues of the differential form Laplacian on a compact Riemannian manifold. The proof uses Alexandrov spaces with curvature bounded below. We also construct differential form Laplacians on Alexandrov spaces. Under a local biLipschitz assumption on the Alexandrov space, which is conjecturally always satisfied, we show that the differential form Laplacian has a compact resolvent. We identify its kernel with an intersection homology group.

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John Lott. 2017-05-23. Eigenvalue estimates and differential form Laplacians on Alexandrov spaces. https://arxiv.org/abs/1705.08400

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