# comparison theorem in a sentence

1. This condition, called the Toponogov's triangle comparison theorem.
2. It is a special case of the Sturm-Picone comparison theorem.
3. S . Y . Cheng used Barta's theorem to derive the eigenvalue comparison theorem.
4. Moreover, the sphere ( for instance ) is spectrally rigid, by Cheng's eigenvalue comparison theorem.
5. His mathematican contributions include comparison theorems of Laplacian eigenvalues on Riemannian manifolds and the maximal diameter theorem in Riemannian geometry.
6. It's difficult to find comparison theorem in a sentence.
7. Until 1987 the only known proof in characteristic zero was however based on the complex analytic proof and the GAGA comparison theorems.
8. It continues with geodesics on Riemannian manifolds, the Jacobi field, Morse index, the Rauch comparison theorems and the Cartan-Hadamard theorem.
9. When the sectional curvature is bounded from above, a corollary to the Rauch comparison theorem yields an analogous statement, but with the reverse inequality.
10. :because if you want to merely find out if it is convergent of divergent, you can use the comparison theorem and prove that a larger function is convergent, or a smaller function is divergent.
11. In differential geometry, lower bounds on the Ricci tensor on a Riemannian manifold allow one to extract global geometric and topological information by comparison ( cf . comparison theorem ) with the geometry of a constant curvature space form.
12. You can either use the maclaurin series and integrate term by term, or you can use another application of the comparison theorem and find a bigger function .-- ?03 : 51, 14 March 2007 ( UTC)
13. Mochizuki's main comparison theorem in Hodge Arakelov theory states ( roughly ) that the space of polynomial functions of degree less than " d " on the universal extension of a smooth elliptic curve in torsion points.
14. It is called a comparison theorem as it is an analogue for Arakelov theory of comparison theorems in cohomology relating de Rham cohomology to singular cohomology of complex varieties or 閠ale cohomology of " p "-adic varieties.
15. It is called a comparison theorem as it is an analogue for Arakelov theory of comparison theorems in cohomology relating de Rham cohomology to singular cohomology of complex varieties or 閠ale cohomology of " p "-adic varieties.
16. More:   1  2

PC Version日本語日本語