| Project/Area Number |
09440040
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Osaka City University, Department of Methematics |
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Principal Investigator |
KASUE Atsushi Osaka City Univ.,Dep. Of Math., Prof, 理学部, 教授 (40152657)
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| Co-Investigator(Kenkyū-buntansha) |
HASHIMOTO Yoshitake Osaka City Univ., Dep. of Math., Assoc. Prof., 理学部, 講師 (20271182)
NISHIO Masaharu Osaka City Univ., Dep. of Math., Assoc. Prof., 理学部, 助教授 (90228156)
KATO Shin Osaka City Univ., Dep. of Math., Assoc. Prof., 理学部, 助教授 (10243354)
KUMURA Hironori Shizuoka Univ., Dep. of Math., Assit, 理学部, 助手 (30283336)
OGURA Yukio Saga Univ., Dep. of Math., Prof., 理工学部, 教授 (00037847)
KOMATSU Takashi Osaka City Univ., Dep. of Math., Prof.
MASUDA Mikiya Osaka City Univ., Dep. of Math., Prof. (00143371)
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| Project Period (FY) |
1997 – 1999
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| Keywords | Riemannian manifold / heat kernel / Gromov-Hausdorff distance / spectral distance / Dirichlet space / parabolic Harnack inequality |
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| Research Abstract |
Riemannian manifolds are considered as metric spaces equipped with Riemannian distances and also Dirichlet spaces endowed with the Riemannian measures and the energy forms ; on a family of such manifolds, the Gromov-Hausdorff distance and the spectral distance induce uniform topologies. The former is concerning the metric structure and the latter is concerning the spectral structure.
In this program, we studied a family of compact, connected Riemannian manifolds such that the heat kernels of manifolds in the family satisfy a uniform on-diagonal estimate from below, and we have established some basic results on (1) the structure of limit spaces of the family from the view-points of Gromov-Hausdorff distance and the spectral distance ; (2) the convergence of energy forms ; (3) the spectral convergence of vector bundle Laplacians ; (4) the convergence of harmonic maps of manifolds in the family to Riemannian manifolds of nonpositive curvature. The volume doubling condition and the Neumann-Poincare inequality, equivalently the parabolic Harnack inequality, play important roles in these investigations.
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