| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
We study the limit of the eigenvalues of the Hodge-Laplacian, when a compact Riemannian manifold collapses. In particular, we study the following collapsing of Riemannian manifolds: we take a compact Riemannian manifold obtained by gluing two compact manifolds with the same boundaries, and one part of the resulting Riemannian manifold uniformly collapses to a point. Then, we prove that all of the positive eigenvalues of the Hodge-Laplacian for collapsing Riemannian manifolds converge to all of those of a suitable Hodge-Laplacian on the limit space. We also obtain an index formula for the multiplicity of eigenvalues which converge to 0.
These results are joint works with Colette Ann'e (Universiet'e de Nantes, in France).
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