Spectral geometry of the form valued Laplacian for manifolds with boundary (Q1183953)

Let \((M^ m,g)\) be a compact oriented Riemannian manifold with boundary, \(D\) an elliptic operator of order \(k\) and \(\sum^ \infty_{n=0}t^{(n- m)/2k}a_ n(D)\) be the asymptotic expansion for the trace of the heat kernel after integration. The authors study this expansion and spectral geometry of the form valued Laplacian with relative, absolute and Clifford boundary conditions and generalize earlier work of Patodi. They also study the asymptotics arising from the eta function which measure spectral asymmetry of \(d+\delta\) with Clifford boundary conditions.