# comparison theorem in a sentence

## SentencesMobile

• 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.
• 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.
• It's difficult to see comparison theorem in a sentence .
• 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.
• If tighter bounds on the sectional curvature are known, then this property generalizes to give a comparison theorem between geodesic triangles in " M " and those in a suitable simply connected space form; see Toponogov's theorem.
• In the theory of differential equations, "'comparison theorems "'assert particular properties of solutions of a differential equation ( or of a system thereof ) provided that an auxiliary equation / inequality ( or a system thereof ) possesses a certain property.
• The functional equation for the zeta function follows from Poincar?duality for " l "-adic cohomology, and the relation with complex Betti numbers of a lift follows from a comparison theorem between " l "-adic and ordinary cohomology for complex varieties.
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