Closed magnetic geodesics on closed hyperbolic Riemann surfaces

TL;DR

This paper proves the existence of special closed curves called magnetic geodesics on hyperbolic surfaces, which are important in understanding geometric and physical properties of these surfaces.

Contribution

It establishes the existence of Alexandrov embedded closed magnetic geodesics on closed hyperbolic surfaces, a new result in geometric analysis.

Findings

Existence of Alexandrov embedded closed magnetic geodesics on hyperbolic surfaces

Characterization of closed magnetic geodesics as curves with prescribed geodesic curvature

Advancement in understanding magnetic geodesics in hyperbolic geometry

Abstract

We prove the existence of Alexandrov embedded closed magnetic geodesics on closed hyperbolic surfaces. Closed magnetic geodesics correspond to closed curves with prescribed geodesic curvature.