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In geometry, a disk (also spelled disc) [1] is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not. [2] For a radius, , an open disk is usually denoted as and a closed disk is ¯.
In particular, the open unit disk is homeomorphic to the whole plane. There is however no conformal bijective map between the open unit disk and the plane. Considered as a Riemann surface, the open unit disk is therefore different from the complex plane. There are conformal bijective maps between the open unit disk and the open upper half-plane ...
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.
In mathematics, the uniformization theorem states that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere.
For example, the solution to the Dirichlet problem for the unit disk in R 2 is given by the Poisson integral formula. If f {\displaystyle f} is a continuous function on the boundary ∂ D {\displaystyle \partial D} of the open unit disk D {\displaystyle D} , then the solution to the Dirichlet problem is u ( z ) {\displaystyle u(z)} given by
A college student just solved a seemingly paradoxical math problem—and the answer came from an incredibly unlikely place. Skip to main content. 24/7 Help. For premium support please call: 800 ...
In mathematics, specifically in functional and complex analysis, the disk algebra A(D) (also spelled disc algebra) is the set of holomorphic functions ƒ : D → C {\displaystyle \mathbb {C} } , (where D is the open unit disk in the complex plane C {\displaystyle \mathbb {C} } ) that extend to a continuous function on the closure of D .
Open disc can refer to: a disk (mathematics) which does not include the circle forming its boundary; the OpenDisc software project This page was last edited on ...