Measure concentration and eigenvalues of Laplacian
【摘要】:Gromov developped a geometric theory of measure concentration,which is useful to study the asymptotic behavior of a sequence of Riemannian manifolds with dimensions going to infinity.Although Gromov omitted the details of proofs,we veryfy some parts of his proofs.Using it,we study the asymptotic behavior of the eigenvalues of the Laplacian if the Riemannian manifolds have nonnegative Ricci curvature.This is a joint work with Kei Funano(RIMS).