Heat Invariants of the Steklov Problem
Heat Invariants of the Steklov Problem
复制标题
DOI：
10.1007/s12220-013-9451-4
复制
发表时间：
2013-04
期刊：
影响因子：
--
通讯作者：
I. Polterovich;David A. Sher
中科院分区：
文献类型：
--
作者：
I. Polterovich;David A. Sher
研究了带边界黎曼流形上Steklov特征值问题的热迹渐近性。特别是，我们描述的Steklov热不变量的结构和计算的前几个明确的标量和平均曲率。这是通过将塞利演算应用于狄利克雷-诺依曼算子来完成的，狄利克雷-诺依曼算子的谱与斯捷克洛夫特征值一致。作为应用，证明了在所有光滑连通边界的欧氏区域中，三维球是由其Steklov谱唯一定义的。
We study the heat trace asymptotics associated with the Steklov eigenvalue problem on a Riemannian manifold with boundary. In particular, we describe the structure of the Steklov heat invariants and compute the first few of them explicitly in terms of the scalar and mean curvatures. This is done by applying the Seeley calculus to the Dirichlet-to-Neumann operator, whose spectrum coincides with the Steklov eigenvalues. As an application, it is proved that a three-dimensional ball is uniquely defined by its Steklov spectrum among all Euclidean domains with smooth connected boundary.