Аннотация:
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 discuss a result in this direction. Joint work
with Dima Dolgopyat.
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