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On non-diffractive cones
- Publication Year :
- 2018
-
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, $\mathbb{R}\mathbb{P}^2$.<br />Comment: Updated in response to referee comments. 13 pages
- Subjects :
- Mathematics - Analysis of PDEs
Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1807.05043
- Document Type :
- Working Paper