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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 4 days ago.

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. $\endgroup$ –

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.

Sep 20, 2022 · 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 ...

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Riemann removable singularity theorem for annuli. Ask Question Asked 10 years, 7 months ago.