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1Department of Biostatistics and Computational Biology, University of Rochester, 601 Elmwood Avenue Box 630, Rochester, New York 14642, USA. Rui_Hu@urmc.rochester.edu or huruizg@hotmail.com
Citation Information: Forum Mathematicum. Volume 21, Issue 6, Pages 1021–1052, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/FORUM.2009.051, September 2009
We study the growth rate of Lp norms of eigenfunctions of the Laplace-Beltrami operator restricted to submanifolds of compact C ∞ Riemannian manifolds. The spectral projection operators can be expressed as oscillatory integral operators, so the question reduces to oscillatory integral operator norm estimates. We study the relationship between the extrinsic geometry of these submanifolds and the canonical relations associated to these oscillatory integral operators.
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