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Selecta Mathematica

, Volume 24, Issue 5, pp 4811–4838 | Cite as

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

  • Baris Coskunuzer
Article
  • 15 Downloads

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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Notes

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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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Mathematics DepartmentBoston CollegeChestnut HillUSA

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