The spectral geometry of flat disks (Q748977)
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scientific article; zbMATH DE number 4171976
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The spectral geometry of flat disks |
scientific article; zbMATH DE number 4171976 |
Statements
The spectral geometry of flat disks (English)
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1990
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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.
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spectral geometry
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heat equation
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flat disks
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planar disks
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Dirichlet or Neumann boundary conditions
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