Abstract
An oriented n-surface S in ℝn +1 is convex (or globally convex) if, for each p ∈ S, S is contained in one of the closed half-spaces
or
where N is the Gauss map of S (see Figure 13.1). An oriented n-surface S is convex at p ∈ S if there exists an open set V ⊂ ℝn +1 containing p such that S ∩ V is contained either in H + p or in H − p . Thus a convex n-surface is necessarily convex at each of its points, but an n-surface convex at each point need not be a convex n-surface (see Figure 13.2).
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© 1979 Springer-Verlag New York Inc.
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Thorpe, J.A. (1979). Convex Surfaces. In: Elementary Topics in Differential Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6153-7_13
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DOI: https://doi.org/10.1007/978-1-4612-6153-7_13
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