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arXiv · 1208.1809

Conic degeneration and the determinant of the Laplacian

David A. Sher
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Abstract

We investigate the behavior of various spectral invariants, particularly the determinant of the Laplacian, on a family of smooth Riemannian manifolds which undergo conic degeneration; that is, which converge in a particular way to a manifold with a conical singularity. Our main result is an asymptotic formula for the determinant up to terms which vanish as the degeneration parameter goes to zero. The proof proceeds in two parts; we study the fine structure of the heat trace on the degenerating manifolds via a parametrix construction, and then use that fine structure to analyze the zeta function and determinant of the Laplacian.

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David A. Sher. 2012-08-09. Conic degeneration and the determinant of the Laplacian. https://arxiv.org/abs/1208.1809

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