BIRS Workshop Lecture Videos
Spectral Rigidity of q-differential Metrics Loving, Marissa
When geometric structures on surfaces are determined by the lengths of curves, it is natural to ask which curvesÃ¢ lengths do we really need to know It is a classical result of Fricke that a hyperbolic metric on a surface is determined by its marked simple length spectrum. More recently, DuchinÃ¢LeiningerÃ¢Rafi proved that a flat metric induced by a unit-norm quadratic differential is also determined by its marked simple length spectrum. In this talk, I will describe a generalization of the notion of simple curves to that of q-simple curves, for any positive integer q, and show that the lengths of q-simple curves suffice to determine a non-positively curved Euclidean cone metric induced by a q-differential metric.
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