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Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)
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Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Christopher D. Sogge

Abstract

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. The book gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace–Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on the geodesic flow. The book shows that there is quantum ergodicity of eigenfunctions if the geodesic flow is ergodic. It begins with a treatment of the Hadamard parametrix before proving the first main result, t ... More

Keywords: eigenfunctions, Riemannian manifolds, Weyl formula, eigenvalues, Laplace–Beltrami operators, Duistermaat-Guillemin theorem, quantum ergodicity, geodesic flow

Bibliographic Information

Print publication date: 2014 Print ISBN-13: 9780691160757
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691160757.001.0001

Authors

Affiliations are at time of print publication.

Christopher D. Sogge, author
Johns Hopkins University