The determinant of the Dirichlet-to-Neumann map for surfaces with boundary
Spectral Theory
2007-08-02 v2
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.
Keywords
Cite
@article{arxiv.math/0701727,
title = {The determinant of the Dirichlet-to-Neumann map for surfaces with boundary},
author = {Colin Guillarmou and Laurent Guillopé},
journal= {arXiv preprint arXiv:math/0701727},
year = {2007}
}
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16 pages