Georgia Institute of Technology College of Sciences

The length spectrum of a Riemannian manifold (M,g) is the set of lengths of closed geodesics on M. A Riemannian metric said to be length spectrum rigid if the any other manifold with the same length spectrum is isometric. Our main result is that all negatively curved metrics whose length spectra satisfy an exponential separation condition are locally length spectrum rigid and therefore locally audible. The main tool is an approximate Livsic theorem with an exponential tail that improves with regularity. This is joint work with Jon DeWitt, James Marshall Reber, and Thomas O'Hare.