The spectral geometry of flat disks
Flat disks \(D_ 1\) and \(D_ 2\) are said to be isometric (resp. piecewise isometric) near the boundary if there are neighborhoods \(N_ 1\) and \(N_ 2\) of \(\partial D_ 1\) and \(\partial D_ 2\) such that \(N_ 1\) is isometric to \(N_ 2\) (resp. \(N_ 1\) can be subdivided into finitely many pieces and rearranged to obtain \(N_ 2)\). The authors show that there exist compact flat disks (resp. planar disks) \(D_ 1\) and \(D_ 2\) which are isometric (resp. piecewise isometric) near the boundary, but which are not isospectral for either Dirichlet or Neumann boundary conditions.
Dirichlet or Neumann boundary conditions
scientific article; zbMATH DE number 4171976