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26 relations: Carathéodory kernel theorem, Carathéodory's theorem (conformal mapping), Cauchy–Schwarz inequality, Charles Loewner, Complex analysis, Complex plane, Conformal field theory, Conformal map, Constantin Carathéodory, De Branges's theorem, Disk (mathematics), Geometric function theory, Holomorphic function, Koebe quarter theorem, Louis de Branges de Bourcia, Mathematics, Oded Schramm, Ordinary differential equation, Picard–Lindelöf theorem, Positive harmonic function, Probability theory, Riemann mapping theorem, Schramm–Loewner evolution, Uniform continuity, Unit disk, Univalent function.
Carathéodory kernel theorem
In mathematics, the Carathéodory kernel theorem is a result in complex analysis and geometric function theory established by the Greek mathematician Constantin Carathéodory in 1912.
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Carathéodory's theorem (conformal mapping)
In mathematics, Carathéodory's theorem is a theorem in complex analysis, named after Constantin Carathéodory, which extends the Riemann mapping theorem.
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Cauchy–Schwarz inequality
In mathematics, the Cauchy–Schwarz inequality, also known as the Cauchy–Bunyakovsky–Schwarz inequality, is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, vector algebra and other areas.
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Charles Loewner
Charles Loewner (29 May 1893 – 8 January 1968) was an American mathematician.
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Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
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Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.
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Conformal field theory
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations.
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Conformal map
In mathematics, a conformal map is a function that preserves angles locally.
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Constantin Carathéodory
Constantin Carathéodory (Greek: Κωνσταντίνος Καραθεοδωρή Konstantinos Karatheodori; 13 September 1873 – 2 February 1950) was a Greek mathematician who spent most of his professional career in Germany.
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De Branges's theorem
In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane.
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Disk (mathematics)
In geometry, a disk (also spelled disc).
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Geometric function theory
Geometric function theory is the study of geometric properties of analytic functions.
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Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
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Koebe quarter theorem
In complex analysis, a branch of mathematics, the Koebe 1/4 theorem states the following: Koebe Quarter Theorem. The image of an injective analytic function f: D → C from the unit disk D onto a subset of the complex plane contains the disk whose center is f(0) and whose radius is |f′(0)|/4.
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Louis de Branges de Bourcia
Louis de Branges de Bourcia (born August 21, 1932) is a French-American mathematician.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Oded Schramm
Oded Schramm (עודד שרם; December 10, 1961 – September 1, 2008) was an Israeli-American mathematician known for the invention of the Schramm–Loewner evolution (SLE) and for working at the intersection of conformal field theory and probability theory.
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Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
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Picard–Lindelöf theorem
In mathematics, in the study of differential equations, the Picard–Lindelöf theorem, Picard's existence theorem or Cauchy–Lipschitz theorem is an important theorem on existence and uniqueness of solutions to first-order equations with given initial conditions.
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Positive harmonic function
In mathematics, a positive harmonic function on the unit disc in the complex numbers is characterized as the Poisson integral of a finite positive measure on the circle.
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Probability theory
Probability theory is the branch of mathematics concerned with probability.
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Riemann mapping theorem
In complex analysis, the Riemann mapping theorem states that if U is a non-empty simply connected open subset of the complex number plane C which is not all of C, then there exists a biholomorphic mapping f (i.e. a bijective holomorphic mapping whose inverse is also holomorphic) from U onto the open unit disk This mapping is known as a Riemann mapping.
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Schramm–Loewner evolution
In probability theory, the Schramm–Loewner evolution with parameter κ, also known as stochastic Loewner evolution (SLEκ), is a family of random planar curves that have been proven to be the scaling limit of a variety of two-dimensional lattice models in statistical mechanics.
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Uniform continuity
In mathematics, a function f is uniformly continuous if, roughly speaking, it is possible to guarantee that f(x) and f(y) be as close to each other as we please by requiring only that x and y are sufficiently close to each other; unlike ordinary continuity, the maximum distance between f(x) and f(y) cannot depend on x and y themselves.
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Unit disk
In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1: The closed unit disk around P is the set of points whose distance from P is less than or equal to one: Unit disks are special cases of disks and unit balls; as such, they contain the interior of the unit circle and, in the case of the closed unit disk, the unit circle itself.
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Univalent function
In mathematics, in the branch of complex analysis, a holomorphic function on an open subset of the complex plane is called univalent if it is injective.
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Loewner chain, Loewner equation, Loewner evolution, Loewner semigroup, Loewner's differential equation, Loewner–Kufarev equation.
References
[1] https://en.wikipedia.org/wiki/Loewner_differential_equation
