无穷远点处与Schr?dinger算子相关的极细集

Minimally thin sets at infinity with respect to the Schr?dinger operator

本文首先得到了一些新的关于锥中无穷远点处与Schr?dinger算子相关极细集的判定准则,其证明是基于对带有修改测度的Green-Sch位势在无穷远点处渐近行为的估计.接着,刻画了这类极细集的几何性质.最后,通过一个反例来说明,所得几何性质的逆命题并不成立.

This paper gives some criterions for minimally thin sets at infinity with respect to the SchrSdinger operator in a cone. Our proofs are based on estimating Green-Sch potential with a positive measure by connecting with a kind of density of the modified measure. Meanwhile, the geometrical property of this minimally thin sets at infinity is also considered. By giving an example, we show that the reverse of this property is not true.