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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 307, Pages 319–327
DOI: https://doi.org/10.4213/tm4044 (Mi tm4044) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Lagrangian Tori and Quantization Conditions Corresponding to Spectral Series of the Laplace Operator on a Surface of Revolution with Conical Points

A. I. Shafarevichabcd

a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
b Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia
c Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526 Russia
d National Research Center “Kurchatov Institute,” pl. Akademika Kurchatova 1, Moscow, 123182 Russia
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DOI: https://doi.org/10.4213/tm4044
Abstract: Semiclassical spectral series of the Laplace operator on a two-dimensional surface of revolution with a conical point are described. It is shown that in many cases asymptotic eigenvalues can be calculated from the quantization conditions on special Lagrangian tori, with the Maslov index of such tori being replaced by a real invariant expressed in terms of the cone apex angle.
Funding agency Grant number
Russian Science Foundation 16-11-10069
This work is supported by the Russian Science Foundation under grant 16-11-10069.
Received: June 1, 2019
Revised: June 12, 2019
Accepted: August 31, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 307, Pages 294–302
DOI: https://doi.org/10.1134/S008154381906018X
Bibliographic databases:
Document Type: Article
UDC: 515.168
Language: Russian
Citation: A. I. Shafarevich, “Lagrangian Tori and Quantization Conditions Corresponding to Spectral Series of the Laplace Operator on a Surface of Revolution with Conical Points”, Algebra, number theory, and algebraic geometry, Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich, Trudy Mat. Inst. Steklova, 307, Steklov Mathematical Institute of RAS, Moscow, 2019, 319–327; Proc. Steklov Inst. Math., 307 (2019), 294–302
Citation in format AMSBIB
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\paper Lagrangian Tori and Quantization Conditions Corresponding to Spectral Series of the Laplace Operator on a Surface of Revolution with Conical Points
\inbook Algebra, number theory, and algebraic geometry
\bookinfo Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich
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\vol 307
\pages 319--327
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
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    • This publication is cited in the following 3 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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