The $a_{3\mathrm{/}2}$ heat kernel coefficient for oblique boundary conditions

We present a method for the calculation of the $a_{3\mathrm{/}2}$ heat kernel coefficient of the heat operator trace for a partial differential operator of Laplace type on a compact Riemannian manifold with oblique boundary conditions. Using special case evaluations, restrictions are put on the general form of the coefficients, which, supplemented by conformal transformation techniques, allows the entire smeared coefficient to be determined.