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

Colin Guillarmou·Laurent Guillopé
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Abstract

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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Colin Guillarmou, Laurent Guillopé. 2007-08-02. The determinant of the Dirichlet-to-Neumann map for surfaces with boundary. https://arxiv.org/abs/math/0701727

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