Convergence of Alexandrov spaces and spectrum of Laplacian

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概要

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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 λ<SUB>k</SUB>(M) the k<SUP>th</SUP> eigenvalue of the Laplacian on M∈ \mathscr{A}(n). We prove the continuity of λ<SUB>k</SUB>.\ \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).

• 社団法人 日本数学会の論文

著者

• Shioya Takashi

  Mathematical Institute Tohoku University

関連論文

• A topological splitting theorem for weighted Alexandrov spaces
• Collapsing three-manifolds with a lower curvature bound
• Convergence of Alexandrov spaces and spectrum of Laplacian

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