On a spin conformal invariant on manifolds with boundary

Simon Raulot (1)

1 IECN - Institut Élie Cartan de Nancy

On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of the Dirac operator under the chiral bag boundary condition. More precisely, we show that we can derive a spinorial analogue of Aubin's inequality.

Mots clés: Manifolds with boundary; Conformally invariant operators; Dirac operator; Chiral bag boundary condition; Yamabe problem

Domaines: Géométrie différentielle [math.DG]

Simon Raulot. On a spin conformal invariant on manifolds with boundary. Mathematische Zeitschrift, 2009, 261 (2), pp.321-349. ⟨10.1007/s00209-008-0327-4⟩. ⟨hal-00098324⟩