论文标题
在恒定的Q曲率指标上具有孤立的奇异性
On constant Q-curvature metrics with isolated singularities
论文作者
论文摘要
在本文中，我们得出了隔离的奇异性附近的精制渐近扩张，用于具有恒定的正q曲面和正标曲率的形式平坦的指标。度量标准具有恒定的Q曲率的条件迫使共形因子与关键的Sobolev生长满足第四阶非线偏微分方程的条件，其领先术语是双乳杆菌。我们将结果对类似的渐近扩展进行了建模，用于由Korevaar，Mazzeo，Pacard和Schoen证明的共形扁平，恒定标态曲率指标。在途中，我们分析了Frank和König最近发现的有关Delaunay指标的Q曲面方程的线性化，这可能具有独立的关注。
In this paper we derive a refined asymptotic expansion, near an isolated singularity, for conformally flat metrics with constant positive Q-curvature and positive scalar curvature. The condition that the metric has constant Q-curvature forces the conformal factor to satisfy a fourth order nonlinear partial differential equation with critical Sobolev growth, whose leading term is the bilaplacian. We model our results on a similar asymptotic expansion for conformally flat, constant scalar curvature metrics proven by Korevaar, Mazzeo, Pacard, and Schoen. Along the way we analyze the linearization of the Q-curvature equation about the Delaunay metrics recently discovered by Frank and König, which may be of independent interest.
