The Boundary Value Problem for Laplacian on Differential Forms and Conformal Einstein Infinity

Abstract

We completely resolve the boundary value problem for differential forms for conformal Einstein infinity in terms of the dual Hahn polynomials. Consequently, we present 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.

Keywords

• Boundary value problems
• Einstein manifolds
• Generalized hypergeometric functions
• Conformal geometry
• Branson- Gover operators
• Q-curvature operators