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Computing the Douady–Earle extension using Kuramoto oscillators

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Abstract

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.

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Acknowledgements

The author wishes to thank his colleague prof. David Kalaj for valuable discussions.

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  1. Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put 2, 81000, Podgorica, Montenegro

    Vladimir Jaćimović

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  1. Vladimir Jaćimović
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Correspondence to Vladimir Jaćimović.

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Jaćimović, V. Computing the Douady–Earle extension using Kuramoto oscillators. Anal.Math.Phys. 9, 523–529 (2019). https://doi.org/10.1007/s13324-018-0214-z

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  • DOI: https://doi.org/10.1007/s13324-018-0214-z

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