极值长度和对偶性

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2025-02-01 DOI:10.1016/j.exmath.2024.125634

Kai Rajala

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引用次数: 0

摘要

经典极值长度（或共形模量）是一个涉及黎曼球上路径族的共形不变量。Fuglede在《极值长度与功能补全》中提出了一种抽象的极值长度理论，并得到了广泛的应用。在对偶性质及其在拟共形分析中的应用方面，我们展示了该理论的灵活性，并在三种不同的情况下给出了最新进展：(1)度量曲面的极值长度和均匀化(2)曲面族的极值长度和n维空间之间的拟共形映射(3)多个连接平面域之间的Schramm跨界极值长度和共形映射。

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Extremal length and duality

Classical extremal length (or conformal modulus) is a conformal invariant involving families of paths on the Riemann sphere. In “Extremal length and functional completion”, Fuglede initiated an abstract theory of extremal length which has since been widely applied. Concentrating on duality properties and applications to quasiconformal analysis, we demonstrate the flexibility of the theory and present recent advances in three different settings:

(1) Extremal length and uniformization of metric surfaces.

(2) Extremal length of families of surfaces and quasiconformal maps between

n

-dimensional spaces.

(3) Schramm’s transboundary extremal length and conformal maps between multiply connected plane domains.

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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