Alexandrov embedded closed magnetic geodesics on S^2
Matthias Schneider
TL;DR
This paper proves that on any two-dimensional sphere with nonnegative Gauss curvature, there are always at least two Alexandrov embedded closed magnetic geodesics, expanding understanding of magnetic geodesic behavior on curved surfaces.
Contribution
It establishes the existence of two such geodesics on spheres with nonnegative Gauss curvature, a new result in geometric analysis of magnetic geodesics.
Findings
Existence of two Alexandrov embedded closed magnetic geodesics on such spheres
Applicable to spheres with nonnegative Gauss curvature
Advances understanding of magnetic geodesic structures on curved surfaces
Abstract
We prove the existence of two Alexandrov embedded closed magnetic geodesics on any two dimensional sphere with nonnegative Gauss curvature.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Analytic and geometric function theory