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Jinsung Park

Publications and source records attributed to Jinsung Park.

23 records · Page 2Linked to original sources
arXiv2005

Adiabatic decomposition of the zeta-determinant and Scattering theory

We discuss the decomposition of the zeta-determinant of the square of the Dirac operator into contributions coming from the different parts of the manifold. The easy case was worked in the previous paper of authors. Due to the assumptions made on the operators in the previous paper, we were able to avoid the presence of the small eigenvalues which provide the large time contibution to the determinant. In the present work we analyze the general case. We offer a detailed analysis of the contribution made by the small eigenvalues.

math.DG↗
arXiv2005

Eta invariants and regularized determinants for odd dimensional hyperbolic manifolds with cusps

We study the eta invariants of Dirac operators and the regularized determinants of Dirac Laplacians over hyperbolic manifolds with cusps. We follow Werner M"uller and use relative traces to define these spectral invariants. We show the regularity of eta and zeta functions at s=0. The Selberg trace formula and the detailed analysis of the unipotent terms give the relation between the eta invariant and the Selberg zeta function of odd type. This allows us to show the vanishing of the unipotent contribution. We show that the eta invariant and the Selberg zeta function of odd type satisfy certain functional equation. These results generalize earlier work of John Millson to hyperbolic manifolds with cusps. We also get the corresponding relation and functional equation for the regularized determinant and the Selberg zeta function of even type where the unipotent factor plays a non-trivial role.

math.DG↗
arXiv2005

Adiabatic decomposition of the zeta-determinant and the Dirichlet to Neumann operator

We prove an adiabatic decomposition formula of the zeta-determinant of the Laplace type operator with respect to Dirichlet boundary condition. We allow the non-invertible tangential operator. As a result, our adiabatic decomposition formula involves the scattering matrix over the manifold with cylindrical end. We also describe the adiabatic limit of the zeta-determinant of the Dirichlet to Neumann operator, which plays the essential role of Burghelea-Friedlander-Kappeler's Meyer-Vietoris type formula of the zeta determinant.

math.DG↗