CR Paneitz算子与CR多重调和函数的稳定性
The CR Paneitz Operator and the Stability of CR Pluriharmonic Functions
摘要：
给出了嵌入三维CR流形的Paneitz算子非负且核仅由CR多重调和函数组成的条件.我们的条件要求Webster数量曲率的一致正性和CR多重调和函数对于实解析变形的稳定性。作为应用，我们证明了$\mathbb{C}^2$中的实椭球使得CR Paneitz算子是非负的，其核仅由CR多重调和函数组成.
英文摘要：
We give a condition which ensures that the Paneitz operator of an embedded three-dimensional CR manifold is nonnegative and has kernel consisting only of the CR pluriharmonic functions. Our condition requires uniform positivity of the Webster scalar curvature and the stability of the CR pluriharmonic functions for a real analytic deformation. As an application, we show that the real ellipsoids in $\mathbb{C}^2$ are such that the CR Paneitz operator is nonnegative with kernel consisting only of the CR pluriharmonic functions.
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