DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, February 14 Padelford C-36 3:45 PM

Conformally invariant non-local operators

A. Rod Gover (University of Auckland and MSRI)

On a conformal manifold with boundary, we construct conformally invariant local boundary conditions B for the conformally invariant power of the Laplacian □_{k}, with the property that (□_{k} , B) is formally self-adjoint. These boundary problems are used to construct conformally invariant non-local operators on the boundary Σ, generalising the conformal Dirichlet-to-Robin operator, with principal parts which are odd powers h (not necessarily positive) of (−Δ_{Σ})^{1/2}, where Δ_{Σ} is the boundary Laplace operator. The constructions use tools from a conformally invariant calculus.

This is collaborative work with Tom Branson (University of Iowa).