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http://dx.doi.org/10.4134/JKMS.2004.41.5.875

THE SPECTRAL GEOMETRY OF EINSTEIN MANIFOLDS WITH BOUNDARY  

Park, Jeong-Hyeong (Department of Computer and Applied Mathematics Honam University)
Publication Information
Journal of the Korean Mathematical Society / v.41, no.5, 2004 , pp. 875-882 More about this Journal
Abstract
Let (M,g) be a compact m dimensional Einstein manifold with smooth boundary. Let $\Delta$$_{p}$,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec($\Delta$$_{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.ant.
Keywords
totally umbillic boundary; totally geodesic boundary; minimal boundary; absolute boundary conditions; relative boundary conditions; Dirichlet Laplacian; Neumann Laplacian.;
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