The zeta-determinant of the Dirichlet-to-Neumann operator on the Steklov eigenvalue problem

초록

On a compact Riemannian manifold with boundary, I’m going to discuss the relation between the zeta-determinant of the Dirichlet-to-Neumann operator on the boundary and the zeta-determinants of Laplacians on the ambient manifold with the Neumann and Dirichlet boundary conditions. I’m also going to use the metric rescaling method to discuss the value of the zeta function at zero associated to the Dirichlet-to-Neumann operator. As an application, on a 2-dimensional compact Riemannian manifold I'm going to show the conformal invariance of the quotient of the zeta-determinant of the Dirichlet-to-Neumann operator divided by the length of the boundary, which was proved earlier by C. Guillarmou and L. Guillop\’e.