Yulin Gong

The spectral concentration for damped waves on compact negatively curved manifolds

We study the spectral distribution of damped waves on compact negatively curved manifolds. Sjöstrand and Anantharaman's work showed that the imaginary parts of most eigenvalues concentrate near the average value of the damping function. In this talk, we prove that most eigenvalues actually lie in certain regions, with imaginary parts approaching the average logarithmically as the real parts tend to infinity. The proof relies on moderate deviation principles for Anosov geodesic flows. As an application, we show that the non-trivial zeros of twisted Selberg zeta functions concentrate in a logarithmic region that is asymptotically close to Re s = 1/2.