The blowup along the diagonal of the spectral function of the Laplacian

Details The blowup along the diagonal of the spectral function of the Laplacian The blowup along the diagonal of the spectral function of the Laplacian

2011-03-07

arxiv.org/abs/1103.1276v3

Mathematics

Differential Geometry

13 pages, 2 figures. v2 Added some comments and additional references. v3 Added references

Scientific paper

We formulate a precise conjecture about the universal behavior near the
diagonal of the spectral function of the Laplacian of a smooth compact Riemann
manifold. We prove this conjecture when the manifold and the metric are real
analytic, and we also present an alternate proof when the manifold is the round
sphere.

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