# Characterization of the Palais-Smale sequences for the conformal Dirac-Einstein problem and applications

## TL;DR

This paper analyzes the behavior of Palais-Smale sequences in the conformal Dirac-Einstein problem, characterizes bubbling phenomena, and proves existence results for solutions, including infinitely many solutions under symmetry conditions.

## Contribution

It provides a detailed characterization of Palais-Smale sequences and establishes new existence results for solutions, including infinitely many, in the conformal Dirac-Einstein setting.

## Key findings

- Characterization of bubbling phenomena in Palais-Smale sequences
- Existence of positive solutions via Aubin type results
- Existence of infinitely many solutions under symmetry assumptions

## Abstract

In this paper we study the Palais-Smale sequences of the conformal Dirac-Einstein problem. After we characterize the bubbling phenomena, we prove an Aubin type result leading to the existence of a positive solution. Then we show the existence of infinitely many solutions to the problem provided that the underlying manifold exhibits certain symmetries.