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The λ>0 case for Δu=λ−c eu type equation on high dimensional spheres
Abstract
Motivated by prescribed Chern scalar curvature problems in complex geometry, we study the equation Δ𝕊N−1V+λ(eV−1)=0 with λ>0 on spheres. For N≥4 and λ>2(N−2) with λ≠2N, we prove the existence of a nonconstant smooth solution that is axially symmetric and symmetric about the equator.
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BibTeX
@misc{li2026case,
title = {{The $λ>0$ case for $Δu=λ-c e^u$ type equation on high dimensional spheres}},
author = {Yuxuan Li and Qiang Niu and Wubin Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28520},
eprint = {2610.28520},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28520},
}
RIS
TY - UNPB
TI - The λ>0 case for Δu=λ−c e^u type equation on high dimensional spheres
AU - Yuxuan Li
AU - Qiang Niu
AU - Wubin Zhou
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28520
UR - https://arxiv.org/abs/2610.28520
AB - Motivated by prescribed Chern scalar curvature problems in complex geometry, we study the equation Δ_𝕊^N−1V+λ(e^V−1)=0 with λ>0 on spheres. For N≥4 and λ>2(N−2) with λ≠2N, we prove the existence of a nonconstant smooth solution that is axially symmetric and symmetric about the equator.
ER -