Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Convergence of Alexandrov spaces and spectrum of Laplacian
Takashi SHIOYA
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2001 年 53 巻 1 号 p. 1-15

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Denote by \mathscr{A}(n) the family of isometry classes of compact n-dimensional Alexandrov spaces with curvature ≥q-1, and λk(M) the kth eigenvalue of the Laplacian on M∈ \mathscr{A}(n). We prove the continuity of λk.\ \mathscr{A}(n)→ \bm{R} with respect to the Gromov-Hausdorff topology for each k, n∈ \bm{N}, and moreover that the spectral topology in-troduced by Kasue-Kumura [{7}], [{8}] coincides with the Gromov-Hausdorff topology on \mathscr{A}(n).
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