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Peer-reviewedCC BYAdvances in Mathematics

Stability of spinorial Sobolev inequalities on Sn

  • Guofang Wang1
  • Mingwei Zhang1,2
  1. 1University of Freiburg, Inst. of Math., Ernst-Zermelo-Str. 1, D-79104 Freiburg, Germany
  2. 2Wuhan University, School of Mathematics and Statistics, 430072 Wuhan, China
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Abstract

The spinorial Sobolev inequality on the unit sphere states with equality if and only if πœ“ ∈ β„³ , the set of all βˆ’ 1 2 -Killing spinors and their conformal transformations. Our main result in this paper is to refine this inequality by establishing a stability inequality As a by-product of our argument, we show that elements in the set β„³ are not optimizers of another spinorial Sobolev inequality unlike expected by experts. They have in fact index 𝑛 + 1 and nullity 2 [ 𝑛 2 ] + 2 .

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Cite

BibTeXRIS
BibTeX
@article{wang2026stability,
  title = {{Stability of spinorial Sobolev inequalities on Sn}},
  author = {Guofang Wang and Mingwei Zhang},
  journal = {Advances in Mathematics},
  year = {2026},
  month = oct,
  doi = {10.1016/j.aim.2026.111318},
  url = {https://doi.org/10.1016/j.aim.2026.111318},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Stability of spinorial Sobolev inequalities on Sn
AU  - Guofang Wang
AU  - Mingwei Zhang
PY  - 2026
DA  - 2026/10/09
JO  - Advances in Mathematics
DO  - 10.1016/j.aim.2026.111318
UR  - https://doi.org/10.1016/j.aim.2026.111318
AB  - The spinorial Sobolev inequality on the unit sphere states with equality if and only if πœ“ ∈ β„³ , the set of all βˆ’ 1 2 -Killing spinors and their conformal transformations. Our main result in this paper is to refine this inequality by establishing a stability inequality As a by-product of our argument, we show that elements in the set β„³ are not optimizers of another spinorial Sobolev inequality unlike expected by experts. They have in fact index 𝑛 + 1 and nullity 2 [ 𝑛 2 ] + 2 .
SN  - 0001-8708
SN  - 1090-2082
ER  -