双曲度量附近的常Q-曲率度量
微分几何
2012-10-16 v2
摘要
设是一个具有光滑定义函数的Poincaré-Einstein流形。在本文中，我们证明在充分接近的渐近双曲度量的共形类中，存在无穷多个具有常-曲率的渐近双曲度量。这些度量由指定常-曲率方程的线性化算子的核中的元素参数化。类似的分析应用于谱理论中出现的一类四阶方程。
引用
@article{arxiv.1205.6355,
title = {Constant Q-curvature metrics near the Hyperbolic metric},
author = {Gang Li},
journal= {arXiv preprint arXiv:1205.6355},
year = {2012}
}
备注
29 pages. It is a correction of last version: A few words are added in Remark 1.1.to be more precise. Two typos in the reference and corrected. A missing weight in the statement of Corollary 2.5.is added. A sign is corrected in the sentence "When $n=4$"in the proof of Lemma 2.6