论文标题
laplacian Vanishing定理用于量化的单数liouville方程式
Laplacian Vanishing Theorem for Quantized Singular Liouville Equation
论文作者
论文摘要
在本文中，我们建立了具有量化奇异源的单数liouville方程的消失定理。如果爆炸序列倾向于在量化的奇异源附近的无限范围，并且爆炸解决方案违反了奇异源周围的球形harnack不平等（非简单爆炸），则系数函数的拉普拉斯人必须倾向于零。这似乎是Liouville方程的第一个二阶估计，并具有量化的来源和非简单爆炸。该结果以及证明的关键思想对于各种应用程序都非常有用。
In this article we establish a vanishing theorem for singular Liouville equation with quantized singular source. If a blowup sequence tends to infinity near a quantized singular source and the blowup solutions violate the spherical Harnack inequality around the singular source (non-simple blow-ups), the Laplacian of a coefficient function must tend to zero. This seems to be the first second order estimates for Liouville equation with quantized sources and non-simple blow-ups. This result as well as the key ideas of the proof would be extremely useful for various applications.
