Cheng's eigenvalue comparison theorem
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Cheng's eigenvalue comparison theorem very generally states that the larger the domain (or measure), the smaller the first eigenvalue.[1] The 1975 theorem is named after S.Y. Cheng and, for geodesic balls, can be generalized to certain tubular domains. This gives application to the infinitesimal volume comparison theory.[2]
See also
References
- [1]
- A Note on the First Eigenvalue of Spherically Symmetric Manifolds
- On Cheng's eigenvalue comparison theorem, G.P. Bessa, J.F. Montenegro.
- Riemannian foliations and eigenvalue comparison
- S.Y. Cheng, Eigenvalue Comparison Theorems and its Geometric Applications Math. Z. 143, 289{297, (1975).
Notes
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