Inverse Nodal Problems

Abstract

It is shown that nodal sequences determine the underlying manifold up to scaling within classes of rectangles with Dirichlet boundary conditions, separable two dimensional tori, two-dimensional flat Klein bottles and flat tori in two and three dimensions.

12 pages, 1 figure

References in corpus (5)

• Nodal domains statistics - a criterion for quantum chaos
• Resolving isospectral "drums" by counting nodal domains
• Can one count the shape of a drum?
• Counting nodal domains on surfaces of revolution
• Remarks on "Resolving isospectral `drums' by counting nodal domains"

Cited by in corpus (8)

• Nodal portraits of quantum billiards: Domains, lines, and statistics
• On the connection between the number of nodal domains on quantum graphs and the stability of graph partitions
• Critical partitions and nodal deficiency of billiard eigenfunctions
• The Nodal Count {0, 1, 2, 3,...} Implies The Graph is a Tree
• Stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count
• Isospectral graphs with identical nodal counts
• Nodal domains of a non-separable problem - the right angled isosceles triangle
• On the Nodal Count Statistics for Separable Systems in any Dimension