Green function and self-adjoint Laplacians on polyhedral surfaces

Kokotov, Alexey; Lagota, Kelvin

doi:10.4153/S0008414X19000336

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Green function and self-adjoint Laplacians on polyhedral surfaces

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Kokotov, Alexey
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.4153/S0008414X19000336
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1902.03232.pdf
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Citation

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

Cite as: https://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.