In Riemannian geometry, Cheng's eigenvalue comparison theorem states in general terms that the larger the domain, the smaller the first Dirichlet eigenvalue of the Laplace–Beltrami operator. This general characterization is not precise, in part because the notion of "size" of the domain must also account for its curvature. The theorem is due to Cheng (1975b). Using geodesic balls, it can be generalized to certain tubular domains.

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  • In Riemannian geometry, Cheng's eigenvalue comparison theorem states in general terms that the larger the domain, the smaller the first Dirichlet eigenvalue of the Laplace–Beltrami operator. This general characterization is not precise, in part because the notion of "size" of the domain must also account for its curvature. The theorem is due to Cheng (1975b). Using geodesic balls, it can be generalized to certain tubular domains.
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  • 1975b
  • Cheng
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  • In Riemannian geometry, Cheng's eigenvalue comparison theorem states in general terms that the larger the domain, the smaller the first Dirichlet eigenvalue of the Laplace–Beltrami operator. This general characterization is not precise, in part because the notion of "size" of the domain must also account for its curvature. The theorem is due to Cheng (1975b). Using geodesic balls, it can be generalized to certain tubular domains.
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  • Cheng's eigenvalue comparison theorem
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