Browsing by Author "Dozier, Benjamin"

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    Closed geodesics on surfaces
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2022) Dozier, Benjamin
    We consider surfaces of three types: the sphere, the torus, and many-holed tori. These surfaces naturally admit geometries of positive, zero, and negative curvature, 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.