The determinant of the Dirichlet-to-Neumann map for surfaces with boundary

Colin Guillarmou (JAD); Laurent Guillop\'e (LMJL)

The determinant of the Dirichlet-to-Neumann map for surfaces with boundary

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arxiv math/0701727 v2 pith:F2KQ6AQQ submitted 2007-01-25 math.SP

Colin Guillarmou (JAD) , Laurent Guillopé (LMJL) This is my paper · ORCID

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keywords boundarycompactdeterminantdirichlet-to-neumannoperatorcomputeconformallydimension

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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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Neumann scalar determinants on constant curvature disks
hep-th 2025-07 conditional novelty 6.0 of 10

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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