The authors study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. They solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions. They also develop a product formula for solving these asymptotic problems in general. The central tools of their approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary. The latter also controls the breaking of conformal invariance in a very strict way by coupling conformally invariant equations to the scale tractor associated with the generalised scale.
Introduction
Bulk conformal geometry and extension problems
Tractor exterior calculus
The exterior calculus of scale
Higher form Proca equations
Obstructions, detours, gauge operators and $Q$-curvature
Appendx A. The ambient manifold
Appendix B. List of common symbols
Bibliography
A. Rod Gover, University of Auckland, New Zealand.
Emanuele Latini, Laboratori Nazinali di Frascati LNF, Italy.
Andrew Waldron, University of California, Davis, CA, USA.
