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Asymptotic plateau problem in \({\mathbb H}^2\times {\mathbb R}\)

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Abstract

We give a fairly complete solution to the asymptotic Plateau Problem for area minimizing surfaces in \({\mathbb H}^2\times {\mathbb R}\). In particular, we identify the collection of Jordan curves in \(\partial _\infty ({\mathbb H}^2\times {\mathbb R})\) which bounds an area minimizing surface in \({\mathbb H}^2\times {\mathbb R}\). Furthermore, we study the similar problem for minimal surfaces, and show that the situation is highly different.

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Acknowledgements

Part of this research was carried out at MIT during my visit. I would like to thank them for their great hospitality. I would like to thank the referee for very valuable remarks.

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Authors and Affiliations

  1. Mathematics Department, Boston College, Chestnut Hill, MA, 02467, USA

    Baris Coskunuzer

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  1. Baris Coskunuzer
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Correspondence to Baris Coskunuzer.

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The author is partially supported by Simons Collaboration Grant, and Royal Society Newton Mobility Grant.

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Coskunuzer, B. Asymptotic plateau problem in \({\mathbb H}^2\times {\mathbb R}\). Sel. Math. New Ser. 24, 4811–4838 (2018). https://doi.org/10.1007/s00029-018-0428-9

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  • DOI: https://doi.org/10.1007/s00029-018-0428-9

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