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In mathematics — specifically, in Riemannian geometry — geodesic convexity is a natural generalization of convexity for sets and functions to Riemannian manifolds. It is common to drop the prefix "geodesic" and refer simply to "convexity" of a set or function. ==Definitions== Let (''M'', ''g'') be a Riemannian manifold. * A subset ''C'' of ''M'' is said to be a geodesically convex set if, given any two points in ''C'', there is a minimizing geodesic contained within ''C'' that joins those two points. * Let ''C'' be a geodesically convex subset of ''M''. A function ''f'' : ''C'' → R is said to be a (strictly) geodesically convex function if the composition :: : is a (strictly) convex function in the usual sense for every unit speed geodesic arc ''γ'' : () → ''M'' contained within ''C''. 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「Geodesic convexity」の詳細全文を読む スポンサード リンク
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