Let g be a scattering metric on a compact manifold X with boundary, ., a smooth metric giving the interior X ◦ the structure of a complete Riemannian manifold with asymptotically conic ends. An example is any compactly supported perturbation of the standard metric on Rn . Consider the operator H = 1 ∆ + V , where ∆ is the positive Laplacian with respect to g and V is a 2 smooth real-valued function on X vanishing to second order at ∂X. Assuming that g is nontrapping, we construct a global parametrix U(z, w, t) for the kernel.
