Russian Mathematical Surveys
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Russian Mathematical Surveys, 2022, Volume 77, Issue 1, Pages 81–97
DOI: https://doi.org/10.1070/RM9916
(Mi rm9916)
 

This article is cited in 1 scientific paper (total in 1 paper)

Spectrum of the Laplace operator on closed surfaces

D. A. Popov

Lomonosov Moscow State University, Belozersky Research Institute of Physico-Chemical Biology
References:
Abstract: A survey is given of classical and relatively recent results on the distribution of the eigenvalues of the Laplace operator on closed surfaces. For various classes of metrics the dependence of the behaviour of the second term in Weyl's formula on the geometry of the geodesic flow is considered. Various versions of trace formulae are presented, along with ensuing identities for the spectrum. The case of a compact Riemann surface with the Poincaré metric is considered separately, with the use of Selberg's formula. A number of results on the stochastic properties of the spectrum in connection with the theory of quantum chaos and the universality conjecture are presented.
Bibliography: 51 titles.
Keywords: spectrum, Laplace operator, Weyl's formula, geodesic flow, trace formulae, quantum chaos, universality conjecture.
Received: 10.01.2020
Russian version:
Uspekhi Matematicheskikh Nauk, 2022, Volume 77, Issue 1(463), Pages 91–108
DOI: https://doi.org/10.4213/rm9916
Bibliographic databases:
Document Type: Article
UDC: 517.984.5
MSC: Primary 58J50; Secondary 11F72
Language: English
Original paper language: Russian
Citation: D. A. Popov, “Spectrum of the Laplace operator on closed surfaces”, Uspekhi Mat. Nauk, 77:1(463) (2022), 91–108; Russian Math. Surveys, 77:1 (2022), 81–97
Citation in format AMSBIB
\Bibitem{Pop22}
\by D.~A.~Popov
\paper Spectrum of the Laplace operator on closed surfaces
\jour Uspekhi Mat. Nauk
\yr 2022
\vol 77
\issue 1(463)
\pages 91--108
\mathnet{http://mi.mathnet.ru/rm9916}
\crossref{https://doi.org/10.4213/rm9916}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461385}
\zmath{https://zbmath.org/?q=an:1487.58030}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2022RuMaS..77...81P}
\transl
\jour Russian Math. Surveys
\yr 2022
\vol 77
\issue 1
\pages 81--97
\crossref{https://doi.org/10.1070/RM9916}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000790547600001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85130437424}
Linking options:
  • https://www.mathnet.ru/eng/rm9916
  • https://doi.org/10.1070/RM9916
  • https://www.mathnet.ru/eng/rm/v77/i1/p91
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:433
    Russian version PDF:113
    English version PDF:87
    Russian version HTML:218
    References:78
    First page:28
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024