球面区域的等谱性质

The isospectral property of spherical domains

该文研究了二维单位球面S^(2)上具有分段光滑、Lipschitz边界的紧区域的等谱性质.在研究中,使用的主要工具是热核的渐近展开的系数给出的谱不变量.证明了S^(2)上区域边界的广义角存在与否是由Laplace算子的谱完全决定的.

Let S^(2)be a 2-dimensional unit sphere.This paper studies the isospectral property of compact domains in S^(2)with piecewise smooth Lipschitz boundary.The main tools are spectral invariants obtained from the coefficients of asymptotic expansion of the heat kernels.The main result is that the existence of generalized corners is determined completely by the spectrum of the Laplacian on the domain in S^(2).