Q-curvature of Weyl structures and Poincar\'e metrics

TL;DR

This paper extends the concept of Branson's Q-curvature to Weyl structures on even-dimensional conformal manifolds using the Fefferman-Graham theorem, exploring their asymptotic behavior on asymptotically hyperbolic manifolds.

Contribution

It introduces a natural extension of Q-curvature to Weyl structures via the bulk-boundary correspondence and Fefferman-Graham theorem.

Findings

Extension of Q-curvature to Weyl structures

Analysis of asymptotic Dirichlet problem for Weyl structures

Connection between bulk geometry and boundary conformal invariants

Abstract

We study an asymptotic Dirichlet problem for Weyl structures on asymptotically hyperbolic manifolds. By the bulk-boundary correspondence, or more precisely by the Fefferman-Graham theorem on Poincar\'e metrics, this leads to a natural extension of the notion of Branson's $Q$-curvature to Weyl structures on even-dimensional conformal manifolds.