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Rigidity of a Q-curvature-type problem on 𝕊N in every dimension N≥3
Abstract
We prove that for every N≥ 3, every solution to the Q-curvature-type problem αPN u + (N−1)!(1−eNu/(∫𝕊N eNudw))=0 on 𝕊N is constant, provided that $ α\ge\frac{1}{2}$ and αnot =1. The proof consists of a spectral gap estimate and pointwise estimates of the normalized density (∫𝕊N eNudw)−1eNu.
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BibTeX
@misc{gui2026rigidity,
title = {{Rigidity of a $Q$-curvature-type problem on $\mathbbS^N$ in every dimension $N\geq3$}},
author = {Changfeng Gui and Yeyao Hu and Tuoxin Li and Juncheng Wei and Zhantong Xie and Zikai Ye},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11338},
eprint = {2610.11338},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11338},
}
RIS
TY - UNPB
TI - Rigidity of a Q-curvature-type problem on 𝕊^N in every dimension N≥3
AU - Changfeng Gui
AU - Yeyao Hu
AU - Tuoxin Li
AU - Juncheng Wei
AU - Zhantong Xie
AU - Zikai Ye
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11338
UR - https://arxiv.org/abs/2610.11338
AB - We prove that for every N≥ 3, every solution to the Q-curvature-type problem αP_N u + (N−1)!(1−e^Nu/(∫_𝕊^N e^Nudw))=0 on 𝕊^N is constant, provided that $ α\ge\frac{1}{2}$ and αnot =1. The proof consists of a spectral gap estimate and pointwise estimates of the normalized density (∫_𝕊^N e^Nudw)^−1e^Nu.
ER -