论文标题
在对称空间中的距离球的完整拉普拉斯光谱
Full Laplace spectrum of distance spheres in symmetric spaces of rank one
论文作者
论文摘要
我们使用谎言理论方法在同质球上明确计算Laplace-beltrami操作员的完整光谱，这些球体是作为一个等级的（紧凑或非绘制）对称空间的地球距离球发生的，并为所有情况提供一个单个统一公式。作为一种应用，我们发现在紧凑的情况下，即嵌入式常数平均曲率球体分叉的半径中，所有共振半径是距离的，即半径，并表明距离球在非碰撞情况下是稳定且局部刚性的。
We use Lie-theoretic methods to explicitly compute the full spectrum of the Laplace--Beltrami operator on homogeneous spheres which occur as geodesic distance spheres in (compact or noncompact) symmetric spaces of rank one, and provide a single unified formula for all cases. As an application, we find all resonant radii for distance spheres in the compact case, i.e., radii where there is bifurcation of embedded constant mean curvature spheres, and show that distance spheres are stable and locally rigid in the noncompact case.
