论文标题
一个人听不到表面的方向性
One can't hear orientability of surfaces
论文作者
论文摘要
本文的主要结果是，一个人无法听到具有边界的表面的可方向性。更确切地说，我们构建了两个具有相同Neumann Spectrum的边界的等光谱平坦表面，一个是可定向的，另一个是不可定向的。为此，我们将Sunada和Buser的方法应用于Orbifolds的框架。在我们的构造中选择一个对称瓷砖，并改编Fefferman的民间传说论点，我们还表明表面具有不同的Dirichlet光谱。这些结果在{\ it C. R. Acad中宣布。科学。巴黎塞尔。 I Math。}，1995年的第320卷，但到目前为止的完整证明仅以预印式出现。
The main result of this paper is that one cannot hear orientability of a surface with boundary. More precisely, we construct two isospectral flat surfaces with boundary with the same Neumann spectrum, one orientable, the other non-orientable. For this purpose, we apply Sunada's and Buser's methods in the framework of orbifolds. Choosing a symmetric tile in our construction, and adapting a folklore argument of Fefferman, we also show that the surfaces have different Dirichlet spectra. These results were announced in the {\it C. R. Acad. Sci. Paris Sér. I Math.}, volume 320 in 1995, but the full proofs so far have only circulated in preprint form.
