Conformal harmonic forms, Branson–Gover operators and Dirichlet problem at infinity
For odd-dimensional Poincaré–Einstein manifolds , we study the set of harmonic -forms (for ) which are (with ) on the conformal compactification of . This set is infinite-dimensional for small but it becomes finite-dimensional if is large enough, and in one-to-one correspondence with the direct sum of the relative cohomology and the kernel of the Branson–Gover [3] differential operators on the conformal infinity . We also relate the set of forms in the kernel of to the conformal...