Eigenfunctions of the Laplacian of a Riemannian Manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates.
The emphasis is on the global methods and the use of Fourier integral operator methods to analyse norms and nodal sets of eigenfunctions..
This book is an introduction to both the local and global analysis of eigenfunctions.
Eigenfunctions of the Laplacian of a Riemannian Manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates