Continuity properties of integral kernels associated with Schroedinger   operators on manifolds
  For Schroedinger operators (including those with magnetic fields) with singular (locally integrable) scalar potentials on manifolds of bounded geometry, we study continuity properties of some related integral kernels: the heat kernel, the Green function, and also kernels of some other functions of the operator. In particular, we show the joint continuity of the heat kernel and the continuity of the Green function outside the diagonal. The proof makes intensive use of the Lippmann-Schwinger equation. 
Jochen Bruening, Vladimir Geyler, Konstantin Pankrashkin