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The CKN inequality for spinors: symmetry and symmetry breaking

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arxiv 2504.16909 v2 pith:BCHBCKJ2 submitted 2025-04-23 math.AP math.FA

Jean Dolbeault , Maria J. Esteban , Rupert L. Frank , Michael Loss This is my paper · ORCID
classification math.APmath.FA
keywords symmetryspinorscasebreakingdeterminepropertiesscalarwhether
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This paper is devoted to Sobolev interpolation inequalities for spinors, with weights of Caffarelli-Kohn-Nirenberg (CKN) type. In view of the corresponding results for scalar functions, a natural question is to determine whether optimal spinors have symmetry properties, or whether spinors with symmetry properties are linearly unstable, in which case we shall say that symmetry breaking occurs. What symmetry means has to be carefully defined and the overall picture turns out to be richer than in the scalar case. So far, no symmetrization technique is available in the spinorial case. We can however determine a range of the parameters for which symmetry holds using a detailed analysis based mostly on spectral methods.

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  1. Symmetry and symmetry breaking in interpolation inequalities for two-dimensional spinors -- Preliminary results

    math.AP 2025-06 conditional novelty 6.0 of 10

    For a two-dimensional spinor Caffarelli-Kohn-Nirenberg inequality, the authors establish an equivalence to an Aharonov-Bohm inequality and provide numerical evidence that symmetry breaking occurs in a larger parameter...

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