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The CR Nirenberg Problem, Part I: Blow-up Analysis and Compactness
Abstract
We establish a priori estimates and compactness results for positive solutions of the CR Nirenberg problem under natural weighted flatness conditions. The proofs combine refined blow-up analysis, Pohozaev identities, and the complete classification of positive entire solutions to the critical CR Yamabe equation recently obtained by Li--Liu--Ma \cite{LLM2026} and Li \cite{L2026}. Existence and degree results are established in our subsequent paper \cite{QTWPartII}.
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BibTeX
@misc{qiang2026nirenberg,
title = {{The CR Nirenberg Problem, Part I: Blow-up Analysis and Compactness}},
author = {Jiechen Qiang and Zhongwei Tang and Heming Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14797},
eprint = {2610.14797},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14797},
}
RIS
TY - UNPB
TI - The CR Nirenberg Problem, Part I: Blow-up Analysis and Compactness
AU - Jiechen Qiang
AU - Zhongwei Tang
AU - Heming Wang
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14797
UR - https://arxiv.org/abs/2610.14797
AB - We establish a priori estimates and compactness results for positive solutions of the CR Nirenberg problem under natural weighted flatness conditions. The proofs combine refined blow-up analysis, Pohozaev identities, and the complete classification of positive entire solutions to the critical CR Yamabe equation recently obtained by Li--Liu--Ma \cite{LLM2026} and Li \cite{L2026}. Existence and degree results are established in our subsequent paper \cite{QTWPartII}.
ER -