无穷型点上Bergman度规的渐近行为

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-05-25 DOI:10.1112/blms.70100

Ravi Shankar Jaiswal

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引用次数: 0

摘要

研究了C n + 1 $\mathbb {C}^{n + 1}$中光滑有界伪凸域的指数平无穷型边界点上Bergman核在对角线上的非切渐近极限，以及Bergman度规及其全纯截面曲率。n∈n $n \in \mathbb {n}$。在证明这些对象满足适当的定位后，我们应用缩放方法来证明我们的结果。

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Asymptotic Behavior of the Bergman Metric at Infinite Type Points

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Asymptotic Behavior of the Bergman Metric at Infinite Type Points

We investigate nontangential asymptotic limits of the Bergman kernel on the diagonal, and the Bergman metric and its holomorphic sectional curvature at exponentially flat infinite-type boundary points of smooth bounded pseudoconvex domains in $C^{n + 1}$ , $n \in N$ . After showing that these objects satisfy the appropriate localizations, we apply the method of scaling to prove our results.