论文标题
Vaserstein距离的增强不确定性原理
An enhanced uncertainty principle for the Vaserstein distance
论文作者
论文摘要
我们改善了Sagiv和Steinerberger的一些最新结果，这些结果量化了以下不确定性原则：对于平均零的函数$ f $，要么零集的功能尺寸，要么将$ f $的正质量的质量运送到负零件的质量必须很大。我们还对拉普拉斯（Laplacian）特征功能的正的运输成本进行了尖锐的上限估计。这证明了Steinerberger的猜想，并提供了特征功能的节点集的大小的下限。
We improve some recent results of Sagiv and Steinerberger that quantify the following uncertainty principle: for a function $f$ with mean zero, either the size of the zero set of the function or the cost of transporting the mass of the positive part of $f$ to its negative part must be big. We also provide a sharp upper estimate of the transport cost of the positive part of an eigenfunction of the Laplacian. This proves a conjecture of Steinerberger and provides a lower bound of the size of the nodal set of the eigenfunction.
