Evidence from large epidemiological studies has supported concern that being born light for gestational age (LiGA) may be detrimental. The incidence of LiGA babies is an important indicator of the health of women of reproductive age in deprived communities. In the assessment of LiGA in the Western Cape, centile charts constructed for populations in other parts of the world are generally used. T...

We prove that a Riemannian manifold (M, g), close enough to the round sphere in the C topology, has uniformly convex injectivity domains — so M appears uniformly convex in any exponential chart. The proof is based on the Ma–Trudinger–Wang nonlocal curvature tensor, which originates from the regularity theory of optimal transport.