Sawyer, N. (2020). Partial marked length spectrum rigidity of negatively curved surfaces. Retrieved from https://doi.org/10.14418/wes01.3.109
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 Riemannian metric on a compact surface is uniquely determined by its marked length spectrum up to isometry. My results show that under certain conditions on the excluded homotopy classes, a partial marked length spectrum also uniquely determines such a metric. It is also known that an inequality between the marked length spectra of two negatively curved Riemannian metrics on a compact surface implies a corresponding inequality between the area with respect to the metrics. I will show that an inequality between the partial marked length spectra is enough to imply the same conclusion.