Published on *Department of Mathematics* (https://math.yale.edu)

September 17, 2019 - 4:15pm

DL 431

The marked length spectrum of a metric on a compact Riemannian manifold records the length of the shortest closed curve in each free homotopy class. It is known that a negatively curved metric on a compact Riemannian manifold is uniquely determined by its marked length spectrum up to isometry. My preliminary results show that under certain conditions on the excluded homotopy classes, a partial marked length spectrum also uniquely determines the metric.