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Functoriality and heat equation asymptotics. (English) Zbl 0790.58042
Szenthe, J. (ed.) et al., Differential geometry and its applications. Proceedings of a colloquium, held in Eger, Hungary, August 20-25, 1989, organized by the János Bolyai Mathematical Society. Amsterdam: North- Holland Publishing Company. Colloq. Math. Soc. János Bolyai. 56, 285-315 (1992).
The author discusses a functorial approach to computing heat equation asymptotics for manifolds with boundary. His setting is rather general, thus the Laplacian on $$p$$-forms, the spin Laplacian, the Dolbeault Laplacian and further operators are included, as well as Dirichlet and Neumann boundary conditions. For various cases explicit formulas are given and invariants calculated.
Note, that beside the “technical part”, the reader finds a short but very nice introduction to the field.
For the entire collection see [Zbl 0764.00002].
Reviewer: N.Jacob (Erlangen)

##### MSC:
 58J37 Perturbations of PDEs on manifolds; asymptotics 58J35 Heat and other parabolic equation methods for PDEs on manifolds 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 58J70 Invariance and symmetry properties for PDEs on manifolds