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The trace of the heat kernel of hyperbolic manifolds of dimension 3. (La trace du noyau de la chaleur des variétés hyperboliques de dimension 3.) (French) Zbl 0882.58051

Séminaire de théorie spectrale et géométrie. Année 1995-1996. St. Martin d’Hères: Univ. de Grenoble I, Institut Fourier, Sémin. Théor. Spectrale Géom., Chambéry-Grenoble. 14, 53-57 (1996).
W. Thurston proved that a complete non-compact hyperbolic 3-manifold \(M_0\) is a limit of a sequence of manifolds \(M_k\) of the same type, with less cusps. Following a technique developed together with J. Jorgenson, the author obtains the behaviour of the trace of the heat kernel for the convergent series \(M_k \rightarrow M_0\).
For the entire collection see [Zbl 0857.00014].

MSC:

58J35 Heat and other parabolic equation methods for PDEs on manifolds
32Q45 Hyperbolic and Kobayashi hyperbolic manifolds
57M50 General geometric structures on low-dimensional manifolds
57M60 Group actions on manifolds and cell complexes in low dimensions
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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