Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function. They are named after Émile Picard. Little...

the Picard–Lindelöf theorem gives a set of conditions under which an initial value problem has a unique solution. It is also known as Picard's existence...

Picard's little theorem states that every nonconstant entire function takes every value in the complex plane, with perhaps one exception. Picard's great...

that the rank of NS(V) is finite is Francesco Severi's theorem of the base; the rank is the Picard number of V, often denoted ρ(V). Geometrically NS(V)...

Little Picard theorem, that an entire non-constant function on the complex plane cannot omit more than one value. This theorem was proved by Picard in 1879...

forth. The theorem was first established by Picard and Goursat using an iterative scheme: the basic idea is to prove a fixed point theorem using the contraction...

can be understood as an abstract formulation of Picard's method of successive approximations. The theorem is named after Stefan Banach (1892–1945) who first...

maps between Riemann surfaces, as detailed in Liouville's theorem and the Little Picard theorem: maps from hyperbolic to parabolic to elliptic are easy...

version of Montel's theorem stated above is the analog of Liouville's theorem, while the second version corresponds to Picard's theorem. Montel space Fundamental...

removable nor a pole, it is called an essential singularity. The Great Picard Theorem shows that such an f {\displaystyle f} maps every punctured open neighborhood...

a function f(z) assumes a value a, as z grows in size, refining the Picard theorem on behaviour close to an essential singularity. The theory exists for...

considered as a generalization of Picard's theorem. Many other Picard-type theorems can be derived from the Second Fundamental Theorem. As another corollary from...

_{0}V)^{\vee }.} For algebraic curves, the Abel–Jacobi theorem implies that the Albanese and Picard varieties are isomorphic. Intermediate Jacobian Albanese...

Holmgren's uniqueness theorem for linear partial differential equations with real analytic coefficients. Picard–Lindelöf theorem, the uniqueness of solutions...

The theorem was first studied in view of work on differential equations by the French mathematicians around Henri Poincaré and Charles Émile Picard. Proving...

Perron–Frobenius theorem (matrix theory) Peter–Weyl theorem (representation theory) Phragmén–Lindelöf theorem (complex analysis) Picard theorem (complex analysis)...

Peano existence theorem, Peano theorem or Cauchy–Peano theorem, named after Giuseppe Peano and Augustin-Louis Cauchy, is a fundamental theorem which guarantees...

conditions (see Looman–Menchoff theorem). Holomorphic functions exhibit some remarkable features. For instance, Picard's theorem asserts that the range of an...

mathematical complex analysis, Schottky's theorem, introduced by Schottky (1904) is a quantitative version of Picard's theorem. It states that for a holomorphic...

and hence is not even continuous, much less analytic. By the great Picard theorem, it attains every complex value (with the exception of zero) infinitely...

Star Trek: The Next Generation episode "The Royale", Captain Picard states that the theorem is still unproven in the 24th century. The proof was released...

necessary concepts and proved a rigorous version of this theorem. Kolchin (1952) extended Picard–Vessiot theory to partial differential fields (with several...

{\displaystyle \mathbb {C} } have unbounded images. The theorem is considerably improved by Picard's little theorem, which says that every entire function whose...

mappings. Springer Verlag. D. Drasin; Pekka Pankka (2015). "Sharpness of Rickman's Picard theorem in all dimensions". Acta Math. Vol. 214. pp. 209–306....

implies surjectivity of f. This is a corollary of Picard's theorem. Another example of reducing theorems about morphisms of finite type to finite fields...

less well-known identities can be deduced in a similar manner. The Picard theorem can be proved using the winding properties of planar Brownian motion...

sheaf cohomology, and description in terms of the Picard functor, was given by Mumford (2008). The theorem states that for any complete varieties U, V and...

the Cauchy–Kovalevskaya theorem (also written as the Cauchy–Kowalevski theorem) is the main local existence and uniqueness theorem for analytic partial differential...

whenever the real part of a {\displaystyle a} is negative. The Picard–Lindelöf theorem, which shows that ordinary differential equations have solutions...

main theorems implies Picard's theorem, and the Second main theorem of Nevanlinna theory. Many other important generalizations of Picard's theorem can...