THE SPECTRAL GEOMETRY OF EINSTEIN MANIFOLDS WITH BOUNDARY

Abstract

Let (M,g) be a compact m dimensional Einstein manifold with smooth boundary. Let <TEX>$\Delta$</TEX><TEX>$_{p}$</TEX>,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec(<TEX>$\Delta$</TEX><TEX>$_{p}$</TEX>,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.