# comparison theorem in a sentence

- This condition, called the Toponogov's triangle
*comparison theorem*. - It is a special case of the Sturm-Picone
*comparison theorem*. - S . Y . Cheng used Barta's theorem to derive the eigenvalue
*comparison theorem*. - Moreover, the sphere ( for instance ) is spectrally rigid, by Cheng's eigenvalue
*comparison theorem*. - His mathematican contributions include
*comparison theorems*of Laplacian eigenvalues on Riemannian manifolds and the maximal diameter theorem in Riemannian geometry. - It's difficult to find
*comparison theorem*in a sentence. - Until 1987 the only known proof in characteristic zero was however based on the complex analytic proof and the GAGA
*comparison theorems*. - It continues with geodesics on Riemannian manifolds, the Jacobi field, Morse index, the Rauch
*comparison theorems*and the Cartan-Hadamard theorem. - When the sectional curvature is bounded from above, a corollary to the Rauch
*comparison theorem*yields an analogous statement, but with the reverse inequality. - :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. - 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. - 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) - 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. - 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. - 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.

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