Ground state Dirac bubbles and Killing spinors

We prove a classification result for ground state solutions of the critical Dirac equation on R-n, n >= 2. By exploiting its conformal covariance, the equation can be posed on the round sphere S-n and the non-zero solutions at the ground level are given byKilling 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.

Automated summary

By exploring the conformal covariance of the Dirac equation, we have proven a classification result for ground state solutions of the critical Dirac equation on R-n, where these solutions are related to Killing spinors and the Yamabe equation for the sphere. This relationship is crucially based on some known classification results.