Conformal Dirac-Einstein equations on manifolds with boundary

TL;DR

This paper investigates Dirac-Einstein equations on manifolds with boundary, focusing on conformal classes, boundary conditions, bubbling phenomena, and establishing inequalities and existence results.

Contribution

It introduces a classification of bubbling phenomena and proves an Aubin-type inequality for Dirac-Einstein equations with boundary conditions.

Findings

Characterization of bubbling phenomena.

Classification of ground state bubbles.

Proof of an Aubin-type inequality and existence results.

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.