The boundary value problem for Laplacian on differential forms and conformally Einstein infinity

TL;DR

This paper solves the boundary value problem for differential forms on conformally Einstein manifolds using dual Hahn polynomials, providing explicit formulas for Branson-Gover operators, Q-curvature, and gauge operators.

Contribution

It introduces a complete solution to the boundary value problem for differential forms on conformally Einstein infinity, with explicit formulas and operator factorizations.

Findings

Explicit formulas for Branson-Gover operators on Einstein manifolds

Representation of operators as products of second order operators

Explicit description of Q-curvature and gauge operators

Abstract

We completely resolve the boundary value problem for differential forms and conformally Einstein infinity in terms of the dual Hahn polynomials. Consequently, we produce explicit formulas for the Branson-Gover operators on Einstein manifolds and prove their representation as a product of second order operators. This leads to an explicit description of $Q$-curvature and gauge companion operators on differential forms.