Solutions of the equation of a spinorial Yamabe-type problem on manifolds of bounded geometry

TL;DR

This paper investigates the existence of solutions to a spinorial Yamabe-type equation on open manifolds with bounded geometry, establishing conditions for existence and implications for the conformal Hijazi inequality.

Contribution

It demonstrates the existence of solutions under certain conditions and links these solutions to the conformal Hijazi inequality on spin manifolds.

Findings

Existence of solutions under specific assumptions

Solution existence implies the conformal Hijazi inequality

Provides new insights into spinorial geometric analysis

Abstract

We consider a spinorial Yamabe-type problem on open manifolds of bounded geometry. The aim is to study the existence of solutions to the associated Euler-Lagrange-equation. We show that under suitable assumptions such a solution exists. As an application, we prove that existence of a solution implies the conformal Hijazi inequality for the underlying spin manifold.