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.

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