论文标题
Meyer-Vietoris公式，用于Riemann表面上的Dirichlet到Neumann操作员的决定因素
A Meyer-Vietoris formula for the determinant of the Dirichlet-to-Neumann operator on Riemann surfaces
论文作者
论文摘要
本文提出了一种迈耶 - 越野式胶合公式，用于带边界的riemannian表面的形式不变的，该表面由Dirichlet到Neumann运算符的决定因素定义。该公式用于结合变性不变的渐近学。结果表明，与大地边界的双曲线表面模量空间上的相关高度函数仅在零属中适当。在零属的情况下，适当性暗示了steklov同一指标的紧凑定理。该公式还为Laplacian的决定因素提供了渐近级或Neumann边界条件。为了证明证明，我们得出了具有外部电势的图形拉普拉奇人的Kirchhoff加权基质树定理的扩展。
This paper presents a Meyer-Vietoris type gluing formula for a conformal invariant of a Riemannian surface with boundary that is defined by the determinant of the Dirichlet-to-Neumann operator. The formula is used to bound the asymptotics of the invariant under degeneration. It is shown that the associated height function on the moduli space of hyperbolic surfaces with geodesic boundary is proper only in genus zero. Properness implies a compactness theorem for Steklov isospectral metrics in the case of genus zero. The formula also provides asymptotics for the determinant of the Laplacian with Dirichlet or Neumann boundary conditions. For the proof, we derive an extension of Kirchhoff's weighted matrix tree theorem for graph Laplacians with an external potential.
