Local Properties of Riesz Minimal Energy Configurations and Equilibrium Measures
Local Properties of Riesz Minimal Energy Configurations and Equilibrium Measures
复制标题
Riesz 最小能量配置的局部性质和平衡措施
DOI：
10.1093/imrn/rnx262
复制
发表时间：
2019
影响因子：
1
通讯作者：
Saff, E.
中科院分区：
文献类型：
--
作者：
Hardin, D.;Reznikov, A.;Saff, E.
我们研究了紧集上离散riesz能量最小的点构型的分离性质。当是无边界和的光滑维流形时，我们证明了分离的顺序（as）是最好的。同样的结论也适用于与任意维集合的边界有固定正距离的点。这些估计扩展了Dahlberg对某些光滑维表面的结果，当（谐波情况下）。此外，对于“贪心”能量点，我们也得到了相同的分离结果。我们从平衡测度（即解决连续最小riesz -能量问题的测度）的上正则性推导出我们的结果，并且我们证明了该性质在集合的局部光滑假设下成立。
We investigate separation properties of-point configurations that minimize discrete Riesz-energy on a compact set. Whenis a smooth-dimensional manifold without boundary and, we prove that the order of separation (as) is the best possible. The same conclusions hold for the points that are a fixed positive distance from the boundary ofwheneveris any-dimensional set. These estimates extend a result of Dahlberg for certain smooth-dimensional surfaces when(the harmonic case). Furthermore, we obtain the same separation results for “greedy”-energy points. We deduce our results from an upper regularity property of the-equilibrium measure (i.e., the measure that solves the continuous minimal Riesz-energy problem), and we show that this property holds under a local smoothness assumption on the set.