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Quantitative Stability for Fractional Yamabe minimizers

  • A. Sophie Aiken
  • Benjamín Borquez
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Abstract

We study quantitative stability for the fractional Yamabe functional introduced by González and Qing. Its minimizers correspond to conformal metrics with constant fractional curvature. We prove that the deficit of the fractional Yamabe functional controls, with a suitable power, the distance to the set of minimizers. Our approach is based on a Lyapunov--Schmidt reduction for the nonlocal functional, together with the extension characterization of the fractional conformal Laplacian, which provides the regularity theory needed for the local analysis. As a consequence, we also obtain an analogous quantitative stability estimate for the associated extension functional.

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Cite

BibTeXRIS
BibTeX
@misc{aiken2026quantitative,
  title = {{Quantitative Stability for Fractional Yamabe minimizers}},
  author = {A. Sophie Aiken and Benjamín Borquez},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00324},
  eprint = {2609.00324},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00324},
}
RIS
TY  - UNPB
TI  - Quantitative Stability for Fractional Yamabe minimizers
AU  - A. Sophie Aiken
AU  - Benjamín Borquez
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00324
UR  - https://arxiv.org/abs/2609.00324
AB  - We study quantitative stability for the fractional Yamabe functional introduced by González and Qing. Its minimizers correspond to conformal metrics with constant fractional curvature. We prove that the deficit of the fractional Yamabe functional controls, with a suitable power, the distance to the set of minimizers. Our approach is based on a Lyapunov--Schmidt reduction for the nonlocal functional, together with the extension characterization of the fractional conformal Laplacian, which provides the regularity theory needed for the local analysis. As a consequence, we also obtain an analogous quantitative stability estimate for the associated extension functional.
ER  -