The Determinant of the Dirichlet-to-Neumann Map for Surfaces with Boundary

  title={The Determinant of the Dirichlet-to-Neumann Map for Surfaces with Boundary},
  author={Colin Guillarmou and Laurent Guillop'e},
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 due 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. 

From This Paper

Topics from this paper.


Publications referenced by this paper.

Determinant of the Neumann Operator on Smooth Jordan Curves.

  • J. Edward, S. Wu
  • Proceedings of the American Mathematical Society…
  • 1991
Highly Influential
6 Excerpts

Einstein Metrics with Prescribed Conformal Infinity on the Ball.

  • C. R. Graham, J. M. Lee
  • Advances in Mathematics 87,
  • 1991
Highly Influential
6 Excerpts

Sur la Distribution des Longueurs des Géodésiques Fermées d’une Surface Compacte à Bord Totalement Géodésique.

  • L. Guillopé
  • Duke Mathematical Journal 53,
  • 1986
Highly Influential
16 Excerpts

Regularity for the Singular Yamabe Problem.

  • R. Mazzeo
  • Indiana University Mathematics Journal 40, no
  • 1991
Highly Influential
11 Excerpts

Compact Isospectral Sets of Surfaces.

  • B. Osgood, R. Phillips, P. Sarnak
  • Journal of Functional Analysis
  • 1988
Highly Influential
5 Excerpts

Spectral Functions, Special Functions and the Selberg Zeta Function.

  • A. Voros
  • Communications in Mathematical Physics
  • 1987
Highly Influential
7 Excerpts

Similar Papers

Loading similar papers…