A commutator method for computation of heat invariants
  We introduce a new method for computing the heat invariants of a 2-dimensional Riemannian manifold based on a result by S.Agmon and Y.Kannai. Two explicit expressions for the heat invariants are presented. The first one depends on the choice of a certain coordinate system; the second involves only invariant terms but has some restrictions on its validity, though in a ``generic'' case it is well-defined. 
Iosif Polterovich