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Reference.org
Geodesic convexity
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> — specifically, in <a href="/facts/Riemannian_geometry/pPEzjyQC">Riemannian geometry</a> — geodesic convexity is a natural generalization of <a href="/facts/Convex_set/vdAuJRJl">convexity for sets</a> and <a href="/facts/Convex_function/IbzG5SLF">functions</a> to <a href="/facts/Riemannian_manifold/5KYnmEgF">Riemannian manifolds</a>. It is common to drop the prefix "geodesic" and refer simply to "convexity" of a set or function. </p>