米伪腔和紧凑性

IF 0.6 3区数学 Q3 MATHEMATICS Analysis Mathematica Pub Date : 2024-04-30 DOI:10.1007/s10476-024-00017-w

O. Günyüz

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引用次数: 0

摘要

最近，谢尔宾娜（Shcherbina）定义了一般复流形中紧凑集的核心，以研究紧凑集上严格多次谐函数的存在性。本文利用非紧凑凯勒流形紧凑子集上的 m 次谐函数，定义了紧凑集的 m 核，并研究了它的结构。我们将对弱m-完全流形的m-最小内核进行分解，并通过作者最近论文中的某些结果，证明它可以完全分解为紧凑的m-伪凹子集，从而对整个凯勒流形（或流形中的域）的m-内核集进行分解，并研究所谓m-斯坦流形的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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m-pseudoconcavity and compactness

The core of a compact set in a general complex manifold has been defined by Shcherbina very recently to study the existence of strictly plurisubharmonic functions on compact sets. In this paper, using m-subharmonic functions on compact subsets of a non-compact Kähler manifold, we define the set m-core of a compact set and investigate the structure of it.

We will have the decomposition of the m-minimal kernel of a weakly m-complete manifold and show that it can be fully decomposed into compact m-pseudoconcave subsets via certain results obtained in the author’s very recent papers to have the disintegration of the set m-core of the entire Kähler manifold (or of a domain in the manifold) and to study the characterization of so-called m-Stein manifolds.

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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.

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