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Harmonic maps between 2-dimensional simplicial complexes: conformal and singular metrics

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Abstract

We study metrics on two-dimensional simplicial complexes that are conformal either to flat Euclidean metrics or to the ideal hyperbolic metrics described by Charitos and Papadopoulos. Extending the results of our previous paper, we prove existence, uniqueness, and regularity results for harmonic maps between two such metrics on a complex.

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Acknowledgements

The authors would like to thank both George Daskalopoulos and Athanase Papadopoulos for suggesting the problem and broader context of the problem, as well as many helpful conversations and suggestions, and the referee for clarifying questions.

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Authors and Affiliations

  1. Auburn University, Auburn, USA

    Brian Freidin

  2. Barcelona, Spain

    Victòria Gras Andreu

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  1. Brian Freidin
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  2. Victòria Gras Andreu
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Both authors contributed to the work leading to, and the writing of this text. VGA prepared all figures. Both authors reviewed the manuscript.

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Correspondence to Brian Freidin.

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Freidin, B., Gras Andreu, V. Harmonic maps between 2-dimensional simplicial complexes: conformal and singular metrics. Geom Dedicata 218, 22 (2024). https://doi.org/10.1007/s10711-023-00871-2

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