2018年3月30日 · Second question. Your question was answered in the discussion in the comments. You are concerned that the annuli are not simply connected, but the extension problem is local, as noticed by taking a small disk in the answer to the question linked to in the comments. The continuity assumption in Schwarz's reflection principle

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2016年6月9日 · Conformal equivalence between annuli. Ask Question Asked 8 years, 8 months ago. Modified 8 years, 8 months ...

2022年9月20日 · All conformal annuli, except $\mathbb{C}-\{p\}$ and $\mathbb{C} - B_{1}(0)$, admit smooth quasiconformal diffeomorphisms between each other. It's worth mentioning that the questions of optimal quasiconformality constants and corresponding extremal mappings (they're exactly the maps you'd hope for) in this setting are a good window into some of ...

2018年6月7日 · Yes, functions can certainly have different expansions in different annuli. A particular expansion is only meaningful for the annulus in which it converges. This is a pretty general result, for holomorphic functions with isolated singularities.

2017年7月28日 · If the all three annuli have a common intersection, that area is selected. See Figure 1: Figure 1. If the annuli overlap each other too much so that there is no common intersection area for all annuli, one area outside the annulus' margins, but are bounded of the annulus' margins, is selected. See Figure 2: Figure 2

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I'm self-studying some complex analysis, and apparently holomorphic bijections between two annuli exist precisely when the ratios of the radii are the same.

2022年11月27日 · The area of the overlap region of two annuli is addressed in Two-Rings. My question adds another annulus/ring to the system. My question adds another annulus/ring to the system. The analogy between two- and three-rings problems is illustrated in Figure: