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 |
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| Дата: | 2009 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2009
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| 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862741750268821504 |
|---|---|
| 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. |
| collection | DSpace DC |
| 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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| first_indexed | 2025-12-07T20:21:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106538 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T20:21:35Z |
| publishDate | 2009 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| 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 |