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S. Y. Cheng
1975
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J. Dodziuk, V. Patodi
1976
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P. Buser, H. Karcher
1981
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Original
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2013

Approximation of the spectrum of a manifold by discretization

Aubry, Erwann

Understand

We approximate the spectral data (eigenvalues and eigenfunctions) of compact Riemannian manifold by the spectral data of a sequence of (computable) discrete Laplace operators associated to some graphs immersed in the manifold.

We give an upper bound on the error that depends on upper bounds on the diameter and the sectional curvature and on a lower bound on the injectivity radius.