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Journal Article

Green function and self-adjoint Laplacians on polyhedral surfaces

MPS-Authors
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Kokotov,  Alexey
Max Planck Institute for Mathematics, Max Planck Society;

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Fulltext (public)

1902.03232.pdf
(Preprint), 295KB

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Citation

Kokotov, A., & Lagota, K. (2020). Green function and self-adjoint Laplacians on polyhedral surfaces. Canadian Mathematical Journal, 72(5), 1324-1351. doi:10.4153/S0008414X19000336.


Cite as: http://hdl.handle.net/21.11116/0000-0007-7BB3-5
Abstract
Using Roelcke 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.