Collapsing of Riemannian manifolds and eigenvalues of Laplace operator

1987/10/01 by Kenji Fukaya · 30 citations
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Topological and Geometric Data Analysis

paper · doi:10.1007/bf01389241

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• Inradius collapsed manifolds with a lower Ricci curvature bound
• Spectral convergence under bounded Ricci curvature
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• Collapsing and Dirac-Type Operators
• Ultralimits of pointed metric measure spaces
• Stability of local Riemannian Ricci curvature lower bounds
• Eigenvalues of Laplacian and multi-way isoperimetric constants on\n weighted Riemannian manifolds
• Gromov's Compactness Theorem for the Intrinsic Timed-Hausdorff Distance
• Periodic Manifolds with Spectral Gaps
• The embedding dimension of Laplacian eigenfunction maps
• Semicontinuity of eigenvalues under intrinsic flat convergence
• Collapsing constant scalar curvature metrics
• H-compactness of elliptic operators on weighted Riemannian Manifolds
• Collapsing and the Differential Form Laplacian : The Case of a Singular Limit Space
• On the scaling limit of finite vertex transitive graphs with large\n diameter
• PL density invariant for type II degenerating K3 surfaces, Moduli compactification and hyperKahler metrics
• Ricci curvature, entropy and optimal transport
• Sharp H "older continuity of tangent cones for spaces with a lower Ricci\n curvature bound and applications
• Ricci curvature and convergence of Lipschitz functions
• Symplectic aspects of the first eigenvalue