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arXiv · 1111.6789

On inaudible properties of broken drums - Isospectrality with mixed Dirichlet-Neumann boundary conditions

Peter Herbrich
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Abstract

We study isospectrality for manifolds with mixed Dirichlet-Neumann boundary conditions and express the well-known transplantation method in graph- and representation-theoretic terms. This leads to a characterization of transplantability in terms of monomial relations in finite groups and allows for the generating of new transplantable pairs from given ones as well as a computer-aided search for isospectral pairs. In particular, we show that the Dirichlet spectrum of a manifold does not determine whether it is connected and that an orbifold can be Dirichlet isospectral to a manifold.

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Peter Herbrich. 2011-11-29. On inaudible properties of broken drums - Isospectrality with mixed Dirichlet-Neumann boundary conditions. https://arxiv.org/abs/1111.6789

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