On the Spectrum of Riemannian Manifolds with Attached Thin Handles

The behavior as ε → 0 of the spectrum of the Laplace Beltrami operator Δε is studied on Rieinannian manifolds depending on a small parameter ε . They consist of a fixed compact manifold with attached handles whose radii tend to zero as ε → 0. We consider two cases: when the number of the handles is...

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Опубліковано в: :Журнал математической физики, анализа, геометрии
Дата:2009
Автор: Khrabustovskyi, A.
Формат: Стаття
Мова:Англійська
Опубліковано: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2009
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/106538
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:On the Spectrum of Riemannian Manifolds with Attached Thin Handles / A. Khrabustovskyi // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 2. — С. 145-169. — Бібліогр.: 9 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Khrabustovskyi, A.
author_facet Khrabustovskyi, A.
citation_txt On the Spectrum of Riemannian Manifolds with Attached Thin Handles / A. Khrabustovskyi // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 2. — С. 145-169. — Бібліогр.: 9 назв. — англ.
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container_title Журнал математической физики, анализа, геометрии
description The behavior as ε → 0 of the spectrum of the Laplace Beltrami operator Δε is studied on Rieinannian manifolds depending on a small parameter ε . They consist of a fixed compact manifold with attached handles whose radii tend to zero as ε → 0. We consider two cases: when the number of the handles is fixed and their lengthes are also fixed and when the number of the handles tend to infinity and their lengthes tend to zero as ε → 0 . For these cases we obtain the operators whose spectrum attracts the spectrum of Δε as ε → 0 .
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last_indexed 2025-12-07T20:21:35Z
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spelling Khrabustovskyi, A.
2016-09-30T07:00:42Z
2016-09-30T07:00:42Z
2009
On the Spectrum of Riemannian Manifolds with Attached Thin Handles / A. Khrabustovskyi // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 2. — С. 145-169. — Бібліогр.: 9 назв. — англ.
1812-9471
https://nasplib.isofts.kiev.ua/handle/123456789/106538
The behavior as ε → 0 of the spectrum of the Laplace Beltrami operator Δε is studied on Rieinannian manifolds depending on a small parameter ε . They consist of a fixed compact manifold with attached handles whose radii tend to zero as ε → 0. We consider two cases: when the number of the handles is fixed and their lengthes are also fixed and when the number of the handles tend to infinity and their lengthes tend to zero as ε → 0 . For these cases we obtain the operators whose spectrum attracts the spectrum of Δε as ε → 0 .
The author is grateful to Prof. E.Ya. Khruslov for setting the problem and his attention paid to this work. The work is partially supported by the Grant for Young Scientists of National Academy of Sciences of Ukraine (No. 20207).
en
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
Журнал математической физики, анализа, геометрии
On the Spectrum of Riemannian Manifolds with Attached Thin Handles
Article
published earlier
spellingShingle On the Spectrum of Riemannian Manifolds with Attached Thin Handles
Khrabustovskyi, A.
title On the Spectrum of Riemannian Manifolds with Attached Thin Handles
title_full On the Spectrum of Riemannian Manifolds with Attached Thin Handles
title_fullStr On the Spectrum of Riemannian Manifolds with Attached Thin Handles
title_full_unstemmed On the Spectrum of Riemannian Manifolds with Attached Thin Handles
title_short On the Spectrum of Riemannian Manifolds with Attached Thin Handles
title_sort on the spectrum of riemannian manifolds with attached thin handles
url https://nasplib.isofts.kiev.ua/handle/123456789/106538
work_keys_str_mv AT khrabustovskyia onthespectrumofriemannianmanifoldswithattachedthinhandles