论文标题
单调定理，用于歧管上的亚谐波函数
A monotonicity theorem for subharmonic functions on manifolds
论文作者
论文摘要
我们提供了尖锐的单调性定理，涉及在流形上的亚谐波函数的分布，可以将其视为不确定性原理的一种新的测量理论形式。为了说明该结果的范围，我们推断了Riemann Sphere，复杂的平面和Poincaré光盘的分析功能的合同性估计，并完整地描述了极端功能，因此，在此主题上提供了许多结果和猜想的统一和启发性的观点，尤其是在Wehrl Enterpopy Expopy和Solove的内置和解决方案上。在这方面，我们通过证明相应的极端仅是相干状态来完全证明SU（2）的猜想。另外，我们表明，以上（全局）估计允许本地对应物，在所有情况下，我们也表征了固定分配度量的极端子集。
We provide a sharp monotonicity theorem about the distribution of subharmonic functions on manifolds, which can be regarded as a new, measure theoretic form of the uncertainty principle. As an illustration of the scope of this result, we deduce contractivity estimates for analytic functions on the Riemann sphere, the complex plane and the Poincaré disc, with a complete description of the extremal functions, hence providing a unified and illuminating perspective of a number of results and conjectures on this subject, in particular on the Wehrl entropy conjecture by Lieb and Solovej. In this connection, we completely prove that conjecture for SU(2), by showing that the corresponding extremals are only the coherent states. Also, we show that the above (global) estimates admit a local counterpart and in all cases we characterize also the extremal subsets, among those of fixed assigned measure.
