Metric Curvature, Folding, and Unique Best Approximation

Source abstract

In this paper, the concepts of metric curvature and folding of a $C^1$-representable manifold in a normed linear space are studied. With certain restrictions on the metric curvature and/or folding, one can obtain a neighborhood of unique best approximation from the manifold, and in some cases, the manifold can be shown to be Chebyshev. Several familiar examples, including some classes of $\gamma$-polynomials, are given.