The continuity and range of the quaternionic Monge-AmpSre operator on quaternionic space
The continuity and range of the quaternionic Monge-AmpSre operator on quaternionic space
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四元空间上四元Monge-AmpSre算子的连续性和范围
DOI：
10.1007/s00209-016-1716-8
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发表时间：
2017
影响因子：
0.8
通讯作者：
Dongrui
中科院分区：
文献类型：
--
作者：
Wan;Dongrui
在本文中，我们使用四元数闭合正电流来建立四元数 Monge-Ampère 算子的多势结果。通过引入新的四元数容量，我们证明了一个充分条件，该条件暗示了四元数蒙日-安培测度的弱收敛性。我们还通过使用 Xing 的方法获得了“容量收敛”的等效条件（Proc Am Math Soc 124(2):457–467, 1996）。作为一个应用，讨论了四元数 Monge-Ampère 算子的范围。
In this paper, we use the quaternionic closed positive currents to establish some pluripotential results for quaternionic Monge–Ampère operator. By introducing a new quaternionic capacity, we prove a sufficient condition which implies the weak convergence of quaternionic Monge–Ampère measures. We also obtain an equivalent condition of “convergence in-capacity” by using methods from Xing (Proc Am Math Soc 124(2):457–467, 1996). As an application, the range of the quaternionic Monge–Ampère operator is discussed.