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PreprintarXiv licencearXiv

On Dolbeault's conjecture

  • Juncheng Wei
  • Zetian Yan
  • Zikai Ye
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Abstract

We prove sharp improved Sobolev inequalities on π•Šn, nβ‰₯3, for antipodally even functions and for axially symmetric functions whose critical density |u|2n/(nβˆ’2) has zero barycenter. In both cases, the Dirichlet coefficient improves by the optimal factor 2βˆ’2/n, while the coefficient of the L2 term remains one. Equality holds precisely for constant functions. The even case resolves a conjecture of Dolbeault (2021).

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Cite

BibTeXRIS
BibTeX
@misc{wei2026dolbeaults,
  title = {{On Dolbeault's conjecture}},
  author = {Juncheng Wei and Zetian Yan and Zikai Ye},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14359},
  eprint = {2610.14359},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14359},
}
RIS
TY  - UNPB
TI  - On Dolbeault's conjecture
AU  - Juncheng Wei
AU  - Zetian Yan
AU  - Zikai Ye
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.14359
UR  - https://arxiv.org/abs/2610.14359
AB  - We prove sharp improved Sobolev inequalities on π•Š^n, nβ‰₯3, for antipodally even functions and for axially symmetric functions whose critical density |u|^2n/(nβˆ’2) has zero barycenter. In both cases, the Dirichlet coefficient improves by the optimal factor 2^βˆ’2/n, while the coefficient of the L^2 term remains one. Equality holds precisely for constant functions. The even case resolves a conjecture of Dolbeault (2021).
ER  -