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In mathematics, the conformal radius is a way to measure the size of a simply connected planar domain ''D'' viewed from a point ''z'' in it. As opposed to notions using Euclidean distance (say, the radius of the largest inscribed disk with center ''z''), this notion is well-suited to use in complex analysis, in particular in conformal maps and conformal geometry. A closely related notion is the transfinite diameter or (logarithmic) capacity of a compact simply connected set ''D'', which can be considered as the inverse of the conformal radius of the complement ''E'' = ''Dc'' viewed from infinity. ==Definition== Given a simply connected domain ''D'' ⊂ C, and a point ''z'' ∈ ''D'', by the Riemann mapping theorem there exists a unique conformal map ''f'' : ''D'' → D onto the unit disk (usually referred to as the uniformizing map) with ''f''(''z'') = 0 ∈ D and ''f''′(''z'') ∈ R+. The conformal radius of ''D'' from ''z'' is then defined as : The simplest example is that the conformal radius of the disk of radius ''r'' viewed from its center is also ''r'', shown by the uniformizing map ''x'' ↦ ''x''/''r''. See below for more examples. One reason for the usefulness of this notion is that it behaves well under conformal maps: if φ : ''D'' → ''D''′ is a conformal bijection and ''z'' in ''D'', then . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「conformal radius」の詳細全文を読む スポンサード リンク
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