Galkowski, J;
Wunsch, J;
(2022)
On non-diffractive cones.
Journal of Differential Geometry
, 120
(3)
pp. 505-518.
10.4310/jdg/1649953486.
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Abstract
A subject of recent interest in inverse problems is whether a corner must diffract fixed frequency waves. We study the related question of which cones [0, ∞) × 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 2π. Moreover, we show that if dim Y = 2, then Y is isometric to either the sphere of radius 1 or its Z^{2} quotient, RP^{2}.
| Type: | Article |
|---|---|
| Title: | On non-diffractive cones |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4310/jdg/1649953486 |
| Publisher version: | https://doi.org/10.4310/jdg/1649953486 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10096036 |
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