Geodesic
Green Function and Self-adjoint Laplacians on Polyhedral Surfaces
Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1324-1351

Voir la notice de l'article provenant de la source Cambridge University Press

Using Roelcke’s formula for the Green function, we explicitly construct a basis in the kernel of the adjoint Laplacian on a compact polyhedral surface $X$ and compute the $S$-matrix of $X$ at the zero value of the spectral parameter. We apply these results to study various self-adjoint extensions of a symmetric Laplacian on a compact polyhedral surface of genus two with a single conical point. It turns out that the behaviour of the $S$-matrix at the zero value of the spectral parameter is sensitive to the geometry of the polyhedron.
DOI : 10.4153/S0008414X19000336
Mots-clés : self-adjoint extension, Laplacian, polyhedral surface 
Kokotov, Alexey; Lagota, Kelvin. Green Function and Self-adjoint Laplacians on Polyhedral Surfaces. Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1324-1351. doi: 10.4153/S0008414X19000336
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