比较定理 the comparison theorem
A Note on Comparison Theorems for Nonnegative Matrices
In Riemannian geometry it is a traditional name for a number of theorems that compare various metrics and provide various estimates in Riemannian geometry.
? Rauch comparison theorem relates the sectional curvature of a Riemannian manifold to
the rate at which its geodesics spread apart. ? Toponogov's theorem ? Myers's theorem
? Hessian comparison theorem ? Laplacian comparison theorem
? Morse–Schoenberg comparison theorem
? Berger comparison theorem, Rauch–Berger comparison theorem, M. Berger, \
Extension of Rauch's Metric Comparison Theorem and some Applications\llinois J. Math., vol. 6 (1962) 700–712
? Berger–Kazdan comparison theorem [2]
? Warner comparison theorem for lengths of N-Jacobi fields (N being a submanifold of a
complete Riemannian manifold) F.W. Warner, \of the Rauch Comparison Theorem to Submanifolds\–356).
? Bishop–Gromov inequality, conditional on a lower bound for the Ricci curvatures (R.L.
Bishop & R. Crittenden, Geometry of manifolds) ? Lichnerowicz comparison theorem ? Eigenvalue comparison theorem
? Cheng's eigenvalue comparison theorem
See also: Comparison triangle
Lyapunov comparison theorem
qualitative analysis of large scale dynamical systems
比较定理 the comparison theorem
