Inverse boundary spectral problem for Riemannian polyhedra

Citation

Kirpichnikova A & Kurylev Y (2012) Inverse boundary spectral problem for Riemannian polyhedra. Mathematische Annalen, 354 (3), pp. 1003-1028. https://doi.org/10.1007/s00208-011-0758-9

Abstract
We consider a Riemannian polyhedron of a special type with a piecewise smooth boundary. The associated Neumann Laplacian defines the boundary spectral data as the set of eigenvalues and restrictions to the boundary of the corresponding eigenfunctions. In this paper we prove that the boundary spectral data prescribed on an open subset of the polyhedron boundary determine this polyhedron uniquely, i.e. up to an isometry.

Keywords
Inverse Problem Gaussian Beam Simplicial Complex Transmission Condition Jump Discontinuity

Journal
Mathematische Annalen: Volume 354, Issue 3