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Annals of Global Analysis and Geometry

, Volume 55, Issue 3, pp 509–528 | Cite as

Embedded loops in the hyperbolic plane with prescribed, almost constant curvature

  • Roberta Musina
  • Fabio ZuddasEmail author
Article
  • 39 Downloads

Abstract

Given a constant \(k>1\) and a real-valued function K on the hyperbolic plane \({\mathbb {H}}^2\), we study the problem of finding, for any \(\varepsilon \approx 0\), a closed and embedded curve \(u^\varepsilon \) in \({\mathbb {H}}^2\) having geodesic curvature \(k+\varepsilon K(u^\varepsilon )\) at each point.

Keywords

Hyperbolic plane Prescribed curvature Energy functional Finite-dimensional reduction 

Notes

Acknowledgements

The authors wish to thank the anonymous referee for her/his careful reading of the manuscript and for the valuable suggestions.

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Dipartimento di Scienze Matematiche, Informatiche e FisicheUniversità di UdineUdineItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità di CagliariCagliariItaly

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