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The CR Nirenberg Problem, Part II: Existence and Topological Degree

  • Jiechen Qiang
  • Zhongwei Tang
  • Heming Wang
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Abstract

This paper is a continuation of Part~I \cite{QTWPartI}, where blow-up analysis and compactness results for the CR Nirenberg problem were established. We prove some existence and degree results for the CR Nirenberg problem on the standard sphere. More precisely, we first prove existence results under antipodal and, more generally, finite-group symmetries. Without symmetry, we derive a Leray--Schauder degree formula under natural flatness conditions, yielding existence results for positive prescribed curvatures with certain homogeneous expansions at critical points. We also obtain Aubin-type inequalities under a vanishing first-moment condition, uniformly near the critical exponent.

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Cite

BibTeXRIS
BibTeX
@misc{qiang2026nirenberg,
  title = {{The CR Nirenberg Problem, Part II: Existence and Topological Degree}},
  author = {Jiechen Qiang and Zhongwei Tang and Heming Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15597},
  eprint = {2610.15597},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15597},
}
RIS
TY  - UNPB
TI  - The CR Nirenberg Problem, Part II: Existence and Topological Degree
AU  - Jiechen Qiang
AU  - Zhongwei Tang
AU  - Heming Wang
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15597
UR  - https://arxiv.org/abs/2610.15597
AB  - This paper is a continuation of Part~I \cite{QTWPartI}, where blow-up analysis and compactness results for the CR Nirenberg problem were established. We prove some existence and degree results for the CR Nirenberg problem on the standard sphere. More precisely, we first prove existence results under antipodal and, more generally, finite-group symmetries. Without symmetry, we derive a Leray--Schauder degree formula under natural flatness conditions, yielding existence results for positive prescribed curvatures with certain homogeneous expansions at critical points. We also obtain Aubin-type inequalities under a vanishing first-moment condition, uniformly near the critical exponent.
ER  -