Séance Séminaire

Séminaire Gaston Darboux

Gaps left by simple closed geodesics on surfaces.

Birman and Series have shown that the simple closed geodesics on a hyperbolic surface are nowhere dense. In the lecture, geometric arguments are used to show that for some constant $r_g$ depending only on $g$, any hyperbolic surface of genus $g$ contains a disc of radius $r_g$ that intersects none of the simple closed geodesics.