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math.DG2026
Spectral Geometry of Hurwitz Spaces with Arbitrary Ramification
Jia-Ming, Liou
We study the Friedrichs Laplacian associated with the pullback of the round metric on \(\mb P^1\) by a nonconstant meromorphic function \(φ:X\to\mb P^1\) on a compact Riemann surfa…
math.DG2026
An Explicit Model for Conic Laplacians on \(\mb P^1\)
Jia-Ming, Liou
We study an explicit model of a conic Laplacian on \(\mb P^1\) with cone angle \(2πn\) at \(0\) and \(\infty\). Using Fourier decomposition, we reduce the eigenvalue equation to a…
math.FA2026
Weyl Curves and Zeta Determinants of Conic Laplacians on Riemann Surfaces
Jia-Ming, Liou
We study self-adjoint realizations of conic Laplacians on compact Riemann surfaces with radial conic metrics whose cone angles are integral multiples of \(2π\). Their critical asym…