Closed geodesics on surfaces

Snapshots of modern mathematics from Oberwolfach

Closed geodesics on surfaces

We consider surfaces of three types: the sphere, the torus, and many-holed tori. These surfaces naturally admit geometries of positive, zero, and negative cur- vature, respectively. It is interesting to study straight line paths, known as geodesics, in these geometries. We discuss the issue of counting closed geodesics; this is particularly rich for hyperbolic (negatively curved) surfaces.

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Mathematical subjects

Geometry and Topology

Connections to other fields

Physics

Author(s)

Benjamin Dozier

License

DOI (Digital Object Identifier)

10.14760/SNAP-2022-013-EN

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snapshot-2022-013.pdf

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