We prove a classification result for ground state solutions of the critical Dirac equation on ℝⁿ, n ≥ 2. By exploiting its conformal covariance, the equation can be posed on the round sphere Sⁿ 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.

Ground state Dirac bubbles and Killing spinors

andrea malchiodi;ruijun wu;william borrelli
2021

Abstract

We prove a classification result for ground state solutions of the critical Dirac equation on ℝⁿ, n ≥ 2. By exploiting its conformal covariance, the equation can be posed on the round sphere Sⁿ 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.
2021
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/82978
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