Conformal Dirac-Einstein equations on manifolds with boundary

Abstract

In this paper we study Dirac-Einstein equations on manifolds with boundary, restricted to a conformal class with constant boundary volume, under chiral bag boundary conditions for the Dirac operator. We characterize the bubbling phenomenon, also classifying ground state bubbles. Finally, we prove an Aubin-type inequality and a related existence result.

40 pages.The first part of the proof of Theorem 1.6 has been rewritten. Minor changes. Final version, to appear on Calc. Var. PDE