论文标题
可以通过听到斯托克斯流的共振来了解边界的区域和总曲率
One can know the area and total curvatures of the boundary by hearing the resonances of a Stokes flow
论文作者
论文摘要
通过计算Stokes流的Dirichlet到Neumann地图的完整符号，我们以$λ$的形式建立了热核痕迹的渐近扩展。我们还提供了一个有用的程序，可以明确计算渐近扩展的所有系数。这些系数是$λ$的steklov光谱不变，它为Stokes流提供了精确的几何信息。特别是，前两个系数表明，边界的面积和（总）平均曲率可以由$λ$的steklov特征值知道。
By calculating full symbol for the Dirichlet-to-Neumann map $Λ$ of a Stokes flow, we establish the asymptotic expansion of the trace of the heat kernel for $Λ$. We also give a useful procedure, by which all coefficients of the asymptotic expansion can be explicitly calculated. These coefficients are the Steklov spectral invariants of $Λ$, which provide precise geometric information of the boundary for the Stokes flow. In particular, the first two coefficients show that the area and (total) mean curvature of the the boundary can be known by the Steklov eigenvalues of $Λ$.
