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The spectral geometry of Einstein manifolds with boundary
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Abstract
Let (M,g) be a compact m dimensional Einstein manifold with smooth boundary. Let ∆p,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec(∆p,B) be the spectrum where each eigenvalue is repeated according to multiplicity. We show that certain geometric properties of the boundary may be spectrally characterized in terms of this data where we fix the Einstein constant.
참고문헌 (6)
- "The asymptotics of the Laplacian on a manifold withboundary" (1990)
- "Asymptotic Formulae in Spectral Geometry" (2003), crc press
- "Curvature and the fundamental solution of the at operator", 34 (1970)
- "Spectral geometry and the Kaehler condition for He rmitian manifoldswith boundary", 337, pp.121~128 (2003)
- "Complex powers of an elliptic operator", 10 (1968)
- "Analytic extension of the trace associated with elliptic boundary problems", 91 (1969)
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