Conformally invariant non-local operators

Thomas Branson and A. Rod Gover

Vol. 201 (2001), No. 1, 19–60

DOI: 10.2140/pjm.2001.201.19

Abstract

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, generalizing 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.

Milestones

Received: 9 November 1999

Published: 1 November 2001