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The basic problem in this paper is that of determining the volume, the surface area, the mean curvature and the Gaussian curvature associated with a general multiply-connected bounded domain in R3 together with Dirichlet, Neumann and impedance boundary conditions on its bounding surface, from complete knowledge of the eigenvalues for the negative Laplacian
, in the
— space, using the asymptotic expansion of the spectral function
for small-time t.
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