On a strong multiplicity one property for the length spectra of even   dimensional compact hyperbolic spaces
  We prove a strong multiplicity one theorem for the length spectrum of compact even dimensional hyperbolic spaces i.e. if all but finitely many closed geodesics for two compact even dimensional hyperbolic spaces have the same length, then all closed geodesics have the same length. 
Chandrasheel Bhagwat, C.S.Rajan
math.NT math.DG