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Documents K. Funano - Eigenvalues of Laplacian and Multi-Way Isoperimetric Constants on Weighted Riemannian...

ar X iv :1 30 7. 39 19 v1 [ ma th. DG ] 15 Ju l 2 01 3 EIGENVALUES OF LAPLACIAN AND MULTI-WAY ISOPERIMETRIC CONSTANTS ON WEIGHTED RIEMANNIAN MANIFOLDS KEI FUNANO Abstract.…

Documents Lecture 4. Proof of Ihara’s Theorem, Edge Zetas, Quantum Chaos

Lecture 4. Proof of Ihara’s Theorem, Edge Zetas, Quantum Chaos Ihara’s Theorem. A=adjacency matrix, Q +I = diagonal matrix of degrees, r=rank fundamental group. Ihara…