Convergence of the heat kernel and the resolvent kernel on degenerating hyperbolic Riemann surfaces of finite volume. (English) Zbl 0853.58099

The authors study the limiting behaviour of the heat kernel on a degenerating family of hyperbolic Riemannian surfaces of finite volume. They prove that the heat kernels from surfaces in such a family converge to the heat kernel associated to the limiting surface.
Reviewer: H.Baum (Berlin)


58J35 Heat and other parabolic equation methods for PDEs on manifolds
35K05 Heat equation
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