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

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.

Theorems numbering has been changed; few misprints were fixed