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Russian Mathematical Surveys, 2001, Volume 56, Issue 6, Pages 1085–1105
DOI: https://doi.org/10.1070/RM2001v056n06ABEH000453 (Mi rm453) 		 
This article is cited in 53 scientific papers (total in 53 papers)

Geometric properties of eigenfunctions

D. Jakobsona, N. S. Nadirashvilia, J. Tothb

a McGill University
b University of Chicago
English version PDF (343 kB) Citations (53)
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DOI: https://doi.org/10.1070/RM2001v056n06ABEH000453
Abstract: We give an overview of some new and old results on geometric properties of eigenfunctions of Laplacians on Riemannian manifolds. We discuss properties of nodal sets and critical points, the number of nodal domains, and asymptotic properties of eigenfunctions in the high-energy limit (such as weak * limits, the rate of growth of $L^p$ norms, and relationships between positive and negative parts of eigenfunctions).
Received: 01.11.2001
Russian version:
Uspekhi Matematicheskikh Nauk, 2001, Volume 56, Issue 6(342), Pages 67–88
DOI: https://doi.org/10.4213/rm453
Bibliographic databases:
Document Type: Article
UDC: 514.74+517.95
MSC: Primary 58C40, 35P20; Secondary 35J05, 81Q50, 58J60, 32Q45, 37D50, 37D40
Language: English
Original paper language: Russian
Citation: D. Jakobson, N. S. Nadirashvili, J. Toth, “Geometric properties of eigenfunctions”, Uspekhi Mat. Nauk, 56:6(342) (2001), 67–88; Russian Math. Surveys, 56:6 (2001), 1085–1105
Citation in format AMSBIB
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    • This publication is cited in the following 53 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:128
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