论文标题
具有有限数量的嵌入特征值的圆柱末端的歧管
Manifolds with cylindrical ends having a finite and positive number of embedded eigenvalues
论文作者
论文摘要
我们构建具有圆柱端的表面，该表面具有有限数量的拉普拉斯特征值，该特征值嵌入其连续光谱中。表面是通过将圆柱端连接到带有孔的双曲线圆环上获得的。据我们所知，这是具有圆柱端的歧管的第一个例子，该末端的特征值数量是有限的和非零的。该结构可以变化，以任意属，并任意大量的特征值。构造的表面还具有连续光谱附近的无共振区域，并且在波动方程式的溶液中长期渐近膨胀。
We construct a surface with a cylindrical end which has a finite number of Laplace eigenvalues embedded in its continuous spectrum. The surface is obtained by attaching a cylindrical end to a hyperbolic torus with a hole. To our knowledge, this is the first example of a manifold with a cylindrical end whose number of eigenvalues is known to be finite and nonzero. The construction can be varied to give examples with arbitrary genus and with an arbitrarily large finite number of eigenvalues. The constructed surfaces also have resonance-free regions near the continuous spectrum and long-time asymptotic expansions of solutions to the wave equation.
