Kahler流形中的核心集
Core Sets in Kahler Manifolds
AI总结：
本文在非紧Kahler流形上研究m-次调和函数的核心集，引入m-核心概念，并证明在维数至少2的Kahler流形中，m≥2的m-调和函数是多次调和函数。
摘要：
本文的主要目标是在（非紧）Kahler流形类上研究m-次调和函数背景下的核心集。通过考虑各类多次调和函数，从不同方面对核心集进行了研究。研究这类集合结构的关键概念之一是伪凹性。更一般地，我们将以m-伪凹集的形式定义相对于m-次调和函数的核心结构，即我们所说的m-核心。在m-次调和函数的背景下，我们定义了m-调和函数，并证明了在$\mathbb{C}^{n},\\,(n \geq 2)$以及更一般地在任何维数至少为2的Kahler流形中，对于$m \geq 2$，m-调和函数是多次调和函数。
英文摘要：
The primary objective of this paper is to study core sets in the setting of m-subharmonic functions on the class of (non-compact) Kahler manifolds. Core sets are investigated in different aspects by considering various classes of plurisubharmonic functions. One of the crucial concepts in studying the structure of this kind of sets is the pseudoconcavity. In a more general way, we will have the structure of core defined with respect to the m-subharmonic functions, which we call m-core in our setting, in terms of m-pseudoconcave sets. In the context of m-subharmonic functions, we define m-harmonic functions and show that, in $\mathbb{C}^{n},\,(n \geq 2)$ and more generally in any Kahler manifold of dimension at least 2, m-harmonic functions are pluriharmonic functions for $m \geq 2$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
