THE C-2 HEAT-KERNEL COEFFICIENT IN THE PRESENCE OF BOUNDARY DISCONTINUITIES

We consider the heat kernel on a manifold whose boundary is piecewise smooth. The set of independent geometrical quantities required to cons truct an expression for the contribution of the boundary discontinuiti es to the C-2 heat-kernel coefficient is derived in the case of a scal ar field with Dirichlet and Robin boundary conditions. The coefficient is then determined using conformal symmetry and evaluation on some sp ecific manifolds. For the Robin case a perturbation technique is also developed and employed. The contributions to the smeared heat-kernel c oefficient and cocycle function are calculated. Some incomplete result s for spinor fields with mixed conditions are also presented.