Ground state Dirac bubbles and Killing spinors

Abstract

We prove a classification result for ground state solutions of the critical Dirac equation on ${\mathbb{R}}^n$, $n\ge 2$. By exploiting its conformal covariance, the equation can be posed on the round sphere ${\mathbb{S}}^n$ and the non-zero solutions at the ground level are given by Killing spinors, up to conformal diffeomorphisms. Moreover, such ground state solutions of the critical Dirac equation are also related to the Yamabe equation for the sphere, for which we crucially exploit some known classification results.

arXiv commentFinal version to appear on Comm. Math. Phys

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Cited by in corpus (3)

• Some properties of Dirac-Einstein bubbles
• Curvature effect in the spinorial Yamabe problem on product manifolds
• Decay of solutions of nonlinear Dirac equations