2015/12/15 by Zhiqin Lu, Julie Rowlett
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Boundary (topology) #Domain (mathematical analysis) #Genus #Holomorphic and Operator Theory #Invariant (physics) #Isospectral #Lipschitz continuity #Mathematical analysis #Mathematical physics #Mathematics #Physics #Piecewise #Pure mathematics #Spectrum (functional analysis) #math-ph #math.AP #math.DG #math.MP #math.SP #msc:35K05 #msc:35P99
paper · pdf · doi:10.1112/blms/bdv094
published as Bull. London Math. Soc., 48, no. 1, (2016), 85-93 · This is the author's original manuscript that was submitted to Bulletin of the London Mathematical Society. A significantly revised final version is published in BLMS
openalex publication_date 2015/12/15 · arxiv created 2020/12/11 · arxiv updated 2020/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.