AI 中文总结
本文证明从完备伪厄米流形到负曲率Kähler流形的\\(\bar\partial_b\\)-调和映射的Schwarz引理，并利用Bochner恒等式和Siu型散度恒等式，在Sasakian源和复双曲目标上分类达到水平界的映射，导出叶状结构、多重调和性和秩刚性。
AI 中文摘要
我们证明了从完备伪厄米流形到负曲率Kähler流形的\\(\bar\partial_b\\)-调和映射的Schwarz引理。对于有界广义膨胀的映射，我们给出了全微分和水平微分的界。对于CR映射，一个耦合的Bochner恒等式产生了依赖于秩的水平估计和Reeb微分的界。在Sasakian源和复双曲目标上，我们分类了达到水平界的映射，通过一点处的亏量以积分形式界定了与等式的偏差，并证明了几乎极值序列的紧性。作为应用，一个Siu型散度恒等式在体积增长条件下产生了叶状结构、多重调和性和秩刚性。
英文摘要
We prove Schwarz lemmas for \(\bar\partial_b\)-harmonic maps from complete pseudo-Hermitian manifolds into K"ahler manifolds of negative curvature. For maps of bounded generalized dilatation we bound the full and the horizontal differential. For CR maps a coupled Bochner identity yields rank-dependent horizontal estimates and a bound for the Reeb differential. On Sasakian sources and complex hyperbolic targets we classify the maps attaining the horizontal bound, bound the deviation from equality in integral form by the deficit at one point, and prove compactness of almost extremal sequences. As an application, a Siu-type divergence identity yields foliation, pluriharmonicity and rank rigidity under volume growth conditions.
