Kernel Asymptotics of Exotic Second-Order Operators

The Navier–Lamé operator of classical elasticity, μ∆v+(λ+μ)∇(∇·v), is the simplest example of a linear differential operator whose second-order terms involve a coupling among the components of a vector-valued function. Similar operators on Riemannian manifolds arise in conformal geometry and in quantum gravity. (In the latter context they have come to be called “nonminimal”, but “exotic” is proposed as a better term.) The heat kernel of such an operator has a short-time expansion in terms of geometrical invariants: K(t, x, x) ≈ (4πt) ∑