混合锥尖奇异度量空间的l2 - poincar - dolbeault引理

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2021-09-02 DOI:10.1142/s1793525321500473

Junchao Shentu, Chen Zhao

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引用次数: 0

摘要

具有锥尖混合奇点的Kähler爱因斯坦度量的存在性近年来受到了广泛的关注。人们相信这种度规会产生重要的几何不变量。我们在狄利克雷和诺伊曼边界条件下计算了它们的[公式:见原文]-Hodge-Frölicher谱序列，并在它们上面检验了纯霍奇结构。结果表明，这些上同调与良好紧化的de Rham上同调是一致的。

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An L2-Poincaré–Dolbeault lemma of spaces with mixed cone-cusp singular metrics

The existence of Kähler Einstein metrics with mixed cone and cusp singularity has received considerable attentions in recent years. It is believed that such kind of metric would give rise to important geometric invariants. We computed their [Formula: see text]-Hodge–Frölicher spectral sequence under the Dirichlet and Neumann boundary conditions and examine the pure Hodge structures on them. It turns out that these cohomologies agree well with the de Rham cohomology of a good compactification.

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来源期刊

Journal of Topology and Analysis MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.