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PreprintarXiv licencearXiv

Surjectivity of real-linear Cauchy--Riemann operators: from the minimal Harder--Narasimhan slope to automatic transversality

  • Qingchun Ji
  • Jun Yao
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Abstract

This paper relates the minimal Harder--Narasimhan slope to the surjectivity of real-linear Cauchy--Riemann operators. We establish a conformally invariant L2 criterion and an asymptotic slope criterion, which yield higher-rank automatic transversality criteria for pseudoholomorphic curves beyond the classical rank-one framework. Applications to pseudoholomorphic spheres in S6 provide quantitative L2 obstructions to the integrability of almost complex structures.

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Cite

BibTeXRIS
BibTeX
@misc{ji2026surjectivity,
  title = {{Surjectivity of real-linear Cauchy--Riemann operators: from the minimal Harder--Narasimhan slope to automatic transversality}},
  author = {Qingchun Ji and Jun Yao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.18997},
  eprint = {2608.18997},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.18997},
}
RIS
TY  - UNPB
TI  - Surjectivity of real-linear Cauchy--Riemann operators: from the minimal Harder--Narasimhan slope to automatic transversality
AU  - Qingchun Ji
AU  - Jun Yao
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2608.18997
UR  - https://arxiv.org/abs/2608.18997
AB  - This paper relates the minimal Harder--Narasimhan slope to the surjectivity of real-linear Cauchy--Riemann operators. We establish a conformally invariant L^2 criterion and an asymptotic slope criterion, which yield higher-rank automatic transversality criteria for pseudoholomorphic curves beyond the classical rank-one framework. Applications to pseudoholomorphic spheres in S^6 provide quantitative L^2 obstructions to the integrability of almost complex structures.
ER  -