论文标题
一个人可以听到鼓的角落
One can hear the corners of a drum
论文作者
论文摘要
我们证明，拐角处的存在或不存在是通过以下意义确定的：任何具有分段平滑Lipschitz边界的简单连接的域都不是任何具有平滑边界的属的连接域。此外，我们证明，在具有Lipschitz的所有领域，分段平滑的边界和固定属中，角落的存在或不存在由光谱唯一决定。这意味着角是基本的几何光谱不变的。一个人可以听到角落。
We prove that the presence or absence of corners is spectrally determined in the following sense: any simply connected domain with piecewise smooth Lipschitz boundary cannot be isospectral to any connected domain, of any genus, which has smooth boundary. Moreover, we prove that amongst all 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.
