Computing the Douady–Earle extension using Kuramoto oscillators
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We demonstrate that the Douady–Earle extension can be computed by solving the specific set of ODE’s. This system of ODE’s has several interpretations in Mathematical Physics, such as Kuramoto model of coupled oscillators or Josephson junction arrays. This method emphasizes the key role of conformal barycenter in some theories of Mathematical Physics. On the other hand, it indicates that variations of Kuramoto model might be used in different problems of computational quasiconformal geometry. The idea can be extended to compute the D–E extension in higher dimensions as well.
KeywordsConformal barycenter Douady–Earle extension Coupled oscillators Kuramoto model
The author wishes to thank his colleague prof. David Kalaj for valuable discussions.
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Conflict of interest
The author declares that he has no conflict of interest.
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