论文标题
4-manifold上的单数开处方$ Q $ curvature方程的分类和先验估计值
Classification and a priori estimates for the singular prescribing $Q$-curvature equation on 4-manifold
论文作者
论文摘要
在$（m，g）$上，紧凑型riemannian $ 4- $歧管，我们考虑了规定的$ q- $曲率方程式在$ m $上定义的，带有有限的单数来源。我们首先证明了在$ \ mathbb r^4 $上定义的单数liouville方程的分类定理，并执行浓度紧凑性分析。然后，我们得出了冒泡解决方案的量化结果，并在某些共形不变不采用一些量化值的假设下建立了先验估计值。此外，我们证明了奇异来源周围的球形竖琴不平等，只要它们的力量不是整数。这种不平等意味着在这种情况下，单数来源是\ emph {隔离的简单吹动点}。
On $(M,g)$ a compact riemannian $4-$manifold we consider the prescribed $Q-$curvature equation defined on $M$ with finite singular sources. We first prove a classification theorem for singular Liouville equations defined on $\mathbb R^4$ and perform a concentration compactness analysis. Then we derive a quantization result for bubbling solutions and establish a priori estimate under the assumption that certain conformal invariant does not take some quantized values. Furthermore we prove a spherical Harnack inequality around singular sources provided their strength is not an integer. Such an inequality implies that in this case singular sources are \emph{isolated simple blow up points}.
