Heat kernel asymptotics on manifolds with conic singularities. (English) Zbl 0981.58022
Summary: The Laplacian acting on \(k\)-forms on a manifold with isolated conic singularities is not in general an essentially selfadjoint operator. The heat kernels for selfadjoint extensions of the Laplacian on these metric spaces are described as functions conormal to a manifold with corners. The heat kernel for a given selfadjoint extension is constructed from the Friedrichs heat kernel. The terms in the difference of the heat trace expansions are shown to supply information parametrizing the extension.
MSC:
| 58J37 | Perturbations of PDEs on manifolds; asymptotics |
Keywords:
short time asymptotics; trace expansion; manifolds with isolated conic singularities; Friedrichs extension; Laplacian; heat kernelsReferences:
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