Heat kernel bounds on manifolds with cusps
β Scribed by E.B Davies; N Mandouvalos
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 450 KB
- Volume
- 75
- Category
- Article
- ISSN
- 0022-1236
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π SIMILAR VOLUMES
We describe the spectrum of the Laplacian on a manifold with asymptotically cusp ends and find asymptotics of a corresponding spectral shift function. Here the spectral shift function is the difference of the eigenvalue counting function and the scattering phase.
We prove a lower bound on the ground state eigenfunction of the Dirichlet Laplacian for horn-shaped and cusped domains. The novelty of the method is that for horn-shaped domains it implies a new result for dimension two, and more importantly, is valid for higher dimensions. Moreover, the same techni