Spectral Geometry of the Laplacian Author_Weiyi Su Paired with a stylistic and

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Spectral Geometry of the Laplacian Author_Weiyi Su Paired with a stylistic andDescription The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is called the spectrum. We describe how the spectrum determines a Riemannian manifold. The continuity of the eigenvalue of the Laplacian, Cheeger and Yau's estimate of the first eigenvalue, the LichnerowiczObata's theorem on the first eigenvalue, the Cheng's estimates of the kth eigenvalues, and PaynePlyaWeinberger's inequality of the Dirichlet eigenvalue of