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



Benjamin Dozier


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Mathematical subjects

Algebra and Number Theory
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics

Connections to other fields

Chemistry and Earth Science
Computer Science
Engineering and Technology
Humanities and Social Sciences
Life Science
Reflections on Mathematics

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