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On non-diffractive cones

Galkowski, J; Wunsch, J; (2020) On non-diffractive cones. Journal of Differential Geometry (In press).

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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, RP2.

Type: Article
Title: On non-diffractive cones
Publisher version: https://intlpress.com/site/pub/pages/journals/item...
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 > 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.ucl.ac.uk/id/eprint/10096036
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