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arXiv · 1505.01043

Wave propagation on Euclidean surfaces with conical singularities. I: Geometric diffraction

G. Austin Ford·Andrew Hassell·Luc Hillairet
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Abstract

We investigate the singularities of the trace of the half-wave group, $\mathrm{Tr} \, e^{-it\sqrt\Delta}$, on Euclidean surfaces with conical singularities $(X,g)$. We compute the leading-order singularity associated to periodic orbits with successive degenerate diffractions. This result extends the previous work of the third author \cite{Hil} and the two-dimensional case of the work of the first author and Wunsch \cite{ForWun} as well as the seminal result of Duistermaat and Guillemin \cite{DuiGui} in the smooth setting. As an intermediate step, we identify the wave propagators on $X$ as singular Fourier integral operators associated to intersecting Lagrangian submanifolds, originally developed by Melrose and Uhlmann \cite{MelUhl}.

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G. Austin Ford, Andrew Hassell, Luc Hillairet. 2015-05-05. Wave propagation on Euclidean surfaces with conical singularities. I: Geometric diffraction. https://arxiv.org/abs/1505.01043

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