Inverse problems in spectral geometry
  In this survey we review positive inverse spectral and inverse resonant results for the following kinds of problems: Laplacians on bounded domains, Laplace-Beltrami operators on compact manifolds, Schr\"odinger operators, Laplacians on exterior domains, and Laplacians on manifolds which are hyperbolic near infinity. 
Kiril Datchev and Hamid Hezari
math.SP math-ph math.AP math.MP