Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
On the Spectrum of Riemannian Manifolds with Attached Thin Handles
Репозиторій DSpace/Manakin
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On the Spectrum of Riemannian Manifolds with Attached Thin Handles
Посилання:
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.
Підтримка:
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).
Дата:
2009
Переглядів:
810
Завантажень:
325
Анотація:
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 .
