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One can hear the corners of a drum

Zhiqin Lu ; Julie Rowlett (Institutionen för matematiska vetenskaper, matematik)
Bulletin of the London Mathematical Society (0024-6093). Vol. 48 (2016), 1, p. 85-93.
[Artikel, refereegranskad vetenskaplig]

We prove that the presence or absence of corners is spectrally determined in the following sense: any simply connected planar domain with piecewise smooth Lipschitz boundary and at least one corner cannot be isospectral to any connected planar domain, of any genus, that has smooth boundary. Moreover, we prove that amongst all planar domains with Lipschitz, piecewise smooth boundary and fixed genus, the presence or absence of corners is uniquely determined by the spectrum. This means that corners are an elementary geometric spectral invariant; one can hear corners.



Denna post skapades 2016-01-13. Senast ändrad 2016-03-16.
CPL Pubid: 230609

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik
Matematisk analys
Geometri

Chalmers infrastruktur