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Mar 30, 2018 · 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

Jun 7, 2018 · 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.

Jun 9, 2016 · Conformal equivalence between annuli. Ask Question Asked 8 years, 9 months ago. Modified 12 days ago.

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.

Nov 30, 2017 · $\begingroup$ @TedShifrin that would be showing if the ratio of the radii are equal then 2 annuli are conformally equivalent, that one is straight forward. the other direction however is the one which im not getting. $\endgroup$ –

The special case of these two annuli is not any easier than the general result. $\endgroup$ – user103402.

Jul 28, 2017 · 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