In mathematics, comparison theorems are theorems whose statement involves comparisons between various mathematical objects of the same type, and often...

In Riemannian geometry, Cheng's eigenvalue comparison theorem states in general terms that when a domain is large, the first Dirichlet eigenvalue of its...

In Riemannian geometry, the Rauch comparison theorem, named after Harry Rauch, who proved it in 1951, is a fundamental result which relates the sectional...

inequality is a comparison theorem in Riemannian geometry, named after Richard L. Bishop and Mikhail Gromov. It is closely related to Myers' theorem, and is the...

comparison theorem, introduced by Christopher Zeeman, gives conditions for a morphism of spectral sequences to be an isomorphism. Comparison theorem—Let...

Toponogov's theorem (named after Victor Andreevich Toponogov) is a triangle comparison theorem. It is one of a family of comparison theorems that quantify...

\Omega _{X/k}} . The Riemann–Roch theorem and its far-reaching generalization, the Grothendieck–Riemann–Roch theorem, contain as a crucial ingredient the...

equations, the Sturm–Picone comparison theorem, named after Jacques Charles François Sturm and Mauro Picone, is a classical theorem which provides criteria...

ordinary differential equation. This theorem was stated by Sergey Chaplygin. It is one of many comparison theorems. Consider an initial value problem:...

theorem (proof theory) Deduction theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem...

to the two endpoints of the line. From the fundamental Laplacian comparison theorem proved earlier by Eugenio Calabi, these functions are both superharmonic...

Cheng's eigenvalue comparison theorem Clifford's theorem on special divisors Cohn-Vossen's inequality Erdős–Mordell inequality Euler's theorem in geometry Gromov's...

provides a comparison theorem that can be used to prove uniqueness of a solution to the initial value problem; see the Picard–Lindelöf theorem. It is named...

functions. The squeeze theorem is used in calculus and mathematical analysis, typically to confirm the limit of a function via comparison with two other functions...

d-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...

made a significant addition to equation theory with his work, Sturm's theorem. Sturm was born in Geneva, France in 1803. The family of his father, Jean-Henri...

from two general theorems on ordinary differential equations, the Sturm Oscillation Theorem and the Sturm-Picone Comparison Theorem. If we denote by u...

In mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature...

theorem – Proof that every structure with certain properties is isomorphic to another structure Comparison theorem List of manifolds List of theorems...

theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem,...

Laplacian comparison theorem and the local Hessian comparison theorem. These are used in the proof of the local version of the Toponogov theorem, and many...

to extract global geometric and topological information by comparison (cf. comparison theorem) with the geometry of a constant curvature space form. This...

Myers's theorem, also known as the Bonnet–Myers theorem, is a celebrated, fundamental theorem in the mathematical field of Riemannian geometry. It was...

Riemannian manifold. Conjugate points Geodesic deviation equation Rauch comparison theorem N-Jacobi field Manfredo Perdigão do Carmo. Riemannian geometry. Translated...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b...

specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients...

special case of Calabi's construction. Calabi found the Laplacian comparison theorem in Riemannian geometry, which relates the Laplace–Beltrami operator...

Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through...