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arXiv · 1807.05043

On non-diffractive cones

Jeffrey Galkowski·Jared Wunsch
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Abstract

A subject of recent interest in inverse problems is whether a corner must diffract fixed frequency waves. We generalize this question somewhat and study cones $[0,\infty)\times Y$ which do not diffract high frequency waves. We prove that if $Y$ is analytic and does not diffract waves at high frequency then every geodesic on $Y$ is closed with period $2\pi$. Moreover, we show that if $\dim Y=2$, then $Y$ is isometric to either the sphere of radius 1 or its $\mathbb{Z}^2$ quotient, $\mathbb{R}\mathbb{P}^2$.

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Jeffrey Galkowski, Jared Wunsch. 2018-07-13. On non-diffractive cones. https://arxiv.org/abs/1807.05043

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