On the Spectrum of Riemannian Manifolds with Attached Thin Handles

Автор(и)

  • A. Khrabustovskyi Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering National Academy of Sciences of Ukraine 47 Lenin Ave., Kharkiv, 61103, Ukraine

Ключові слова:

homogenization, Laplace-Beltrami operator, spectrum, Riemannian manifold.

Анотація

The behavior as e → 0 of the spectrum of the Laplace-Beltrami operator De is studied on Riemannian manifolds depending on a small parameter e. They consist of a fixed compact manifold with attached handles whose radii tend to zero as e → 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 e → 0. For these cases we obtain the operators whose spectrum attracts the spectrum of De as e → 0.

Mathematics Subject Classification: 35B27, 35P20, 58G25, 58G30.

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Опубліковано

2009-04-29

Як цитувати

(1)
Khrabustovskyi, A. On the Spectrum of Riemannian Manifolds With Attached Thin Handles. J. Math. Phys. Anal. Geom. 2009, 5, 145-169.

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