Canzani, Y;
Galkowski, J;
Toth, JA;
(2018)
Averages of Eigenfunctions Over Hypersurfaces.
Communications in Mathematical Physics
, 360
(2)
pp. 619-637.
10.1007/s00220-017-3081-9.
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Abstract
Let (M, g) be a compact, smooth, Riemannian manifold and { ϕh} an L^{2}-normalized sequence of Laplace eigenfunctions with defect measure μ. Let H be a smooth hypersurface with unit exterior normal ν. Our main result says that when μ is not concentrated conormally to H, the eigenfunction restrictions to H satisfy∫_{H}ϕhdσH=o(1)and∫_{H}hDνϕhdσH=o(1),h→ 0^{+}.
| Type: | Article |
|---|---|
| Title: | Averages of Eigenfunctions Over Hypersurfaces |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00220-017-3081-9 |
| Publisher version: | https://doi.org/10.1007/s00220-017-3081-9 |
| 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.ucl.ac.uk/id/eprint/10083902 |
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