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The determinant of the Dirichlet-to-Neumann map for surfaces with boundary
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For any orientable compact surface with boundary, we compute the regularized determinant of the Dirichlet-to-Neumann (DN) map in terms of particular values of dynamical zeta functions by using natural uniformizations, one due to Mazzeo-Taylor, the other to Osgood-Phillips-Sarnak. We also relate in any dimension the DN map for the Yamabe operator to the scattering operator for a conformally compact related problem by using uniformization.
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Cited by 2 Pith papers
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The determinant of the Dirichlet-to-Neumann map for a surface with boundary and periods of holomorphic differentials on its double
The zeta determinant of the Dirichlet-to-Neumann map of a surface with boundary equals the determinant of the discrete part of its boundary Hilbert transform, a product of period ratios on the double surface.
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Neumann scalar determinants on constant curvature disks
Neumann determinants of the massive Laplacian on constant curvature disks are expressed as convergent infinite series, with exact special-mass reductions for m^2 = -η/L^2 q(q+1).
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