Singular Yamabe problem, residue families and conformal hypersurface invariants

Lundi 10 février 14:00-15:00 - Andreas Juhl - Humboldt-Universität Berlin

Résumé : We describe recent progress on constructions of natural conformally invariant differential operators which are associated to hypersurfaces in Riemannian manifolds. The constructions rest on the solution of a singular version of the Yamabe problem. We outline two basic approaches. The first rests on conformal tractor calculus (Gover-Waldron) and the second generalizes the notion of residue families (introduced by the author) which involves the Feffermann-Graham Poincaré-Einstein metric. We prove the equivalence of both methods. Both constructions are curved analogs of symmetry breaking operators in representation theory (Kobayashi). Among many things, this naturally leads to a notion of extrinsic Q-curvature which generalizes Branson’s Q-curvature. The presentation will describe work of Gover-Waldron, Graham, Juhl-Orsted and others.

Lieu : IMO ; salle 3L8.

Singular Yamabe problem, residue families and conformal hypersurface invariants  Version PDF