用无穷多权的技术对q-凸流形上Hörmander定理的变型

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2021-04-26 DOI:10.1007/s12188-021-00237-z

Takeo Ohsawa

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引用次数: 2

摘要

通过在算子的（L^2）理论中引入一种新的逼近技术，在q-凸流形和弱1-完全流形上推广和精化了Andreotti-Grauert有限性定理的Hörmander变式。作为一个应用，解决了上田（Tohoku Math J（2）31（1）:81–901979），上田（J Math Kyoto Univ 22（4）:583–6071982/83）的一个理论提出的关于\（L^2）上同调的问题。

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Variants of Hörmander’s theorem on q-convex manifolds by a technique of infinitely many weights

By introducing a new approximation technique in the \(L^2\) theory of the \(\bar{\partial }\)-operator, Hörmander’s \(L^2\) variant of Andreotti-Grauert’s finiteness theorem is extended and refined on q-convex manifolds and weakly 1-complete manifolds. As an application, a question on the \(L^2\) cohomology suggested by a theory of Ueda (Tohoku Math J (2) 31(1):81–90, 1979), Ueda (J Math Kyoto Univ 22(4):583–607, 1982/83) is solved.

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来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.