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

Roberta Musina; Fabio Zuddas

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

Differential Geometry 2018-03-20 v2

Authors: Roberta Musina , Fabio Zuddas

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 $\epsilon\approx 0$ , a closed and embedded curve $u^\epsilon$ in $\mathbb H^2$ having geodesic curvature $k+\epsilon K(u^\epsilon)$ at each point.

Keywords

embedded loops hyperbolic plane geodesic curvature prescribed curvature almost constant curvature

Cite

@article{arxiv.1803.00856,
  title  = {Embedded loops in the hyperbolic plane with prescribed, almost constant curvature},
  author = {Roberta Musina and Fabio Zuddas},
  journal= {arXiv preprint arXiv:1803.00856},
  year   = {2018}
}

Comments

Theorems numbering has been changed; few misprints were fixed

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