Cheng's eigenvalue comparison theorem

Cheng's eigenvalue comparison theorem very generally states that the larger the domain (or measure), the smaller the first eigenvalue. 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.

See also

• Comparison theorem
• Eigenvalue comparison theorem

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).