On small gaps in the length spectrum

05/09/2016 - 15:30
Dmitry Jakobson, McGill University
McGill, Burnside Hall, 805 Sherbrooke Str West, Room 920

 This is joint work with Dmitry Dolgopyat.  We discuss upper and lower bounds for the size of gaps in the length spectrum of negatively curved manifolds. For manifolds with algebraic generators for the fundamental group, we establish the existence of exponential lower bounds for the gaps.
On the other hand, we show that the existence of arbitrary small gaps is topologically generic: this is established both for
surfaces of constant negative curvature, and for the space of negatively curved metrics. While arbitrary small gaps are topologically generic, it is plausible that the gaps are not too small for almost every metric.  We present a result in that direction.  

Last edited by on Mon, 05/09/2016 - 15:41