发表机构
University of Tsukuba（筑波大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在闭伪厄米流形上建立临界CR GJMS算子的下界，利用海森堡微积分和平方根构造，证明三维CR Paneitz算子有下界，并揭示Rossi球上该算子负特征值以零为唯一聚点。
AI 中文摘要
我们在闭伪厄米流形上建立了临界CR GJMS算子的下界。在维数$2n+1$中，假设可嵌入性，我们在核的正交补上，模去一个$L^{2}$项，得到了一个涉及$n+1$阶海森堡Sobolev范数的下界。在三维中，我们证明了CR Paneitz算子在不假设可嵌入性的情况下有下界。证明结合了海森堡微积分与基于海森堡群上子拉普拉斯算子和Reeb向量场的联合泛函演算的平方根构造。作为应用，我们证明了Rossi球上CR Paneitz算子的无穷多个负特征值以零为唯一聚点。因此，该算子不具有闭值域。
英文摘要
We establish lower bounds for the critical CR GJMS operator on closed pseudo-Hermitian manifolds. In dimension $2n+1$, assuming embeddability, we obtain a lower bound involving the Heisenberg Sobolev norm of order $n+1$, modulo an $L^{2}$ term, on the orthogonal complement of the kernel. In dimension three, we prove that the CR Paneitz operator is bounded below without assuming embeddability. The proofs combine the Heisenberg calculus with a square-root construction based on the joint functional calculus of the sub-Laplacian and the Reeb vector field on the Heisenberg group. As an application, we show that the infinitely many negative eigenvalues of the CR Paneitz operator on the Rossi sphere have zero as their only accumulation point. Consequently, this operator does not have closed range.
Comments20 pages
