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.
|Number of pages||30|
|Journal||Communications in Mathematical Physics|
|Publication status||Published - 2021|
- Dirac bubbles