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I would say that a "kink" or a "corner" is a point on a (continuous) line where it is non-differentiable. But I'm at a loss of words when trying to generalize this (in a similarly accessible manner) to higher dimensions.

Formally, I can define what I mean: Take any convex and continuous set in $n+1$ dimensions, and look at its surface. It will look smooth wherever there's a unique tangent hyperplane, but it may have "edges" or "corners" where you could place more than one supporting hyperplane. I want to refer to all such points that have multiple supporting hyperplanes.

Problem is, "edges" somehow makes me think of straight lines, and "corners" makes me think of zero-dimensional subsets. So what term would you use to describe this (something simple that fits into the discussion section of a general-interest economics paper)?

mimuller
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    You may be interested in the concept of "manifold with corners". An open ball is a 3D manifold. A closed ball is a 3D "manifold with boundary" (with its 2D sphere boundary). A solid cube with its edges and vertices is a "manifold with corners" and I think its edges would count as part of the "corners" (in that they couldn't be part of a "manifold with boundary", anyway) – Mark S. Jul 10 '21 at 13:41
  • thanks, but I was hoping for something more informal... I think the readers will take cover if I start talking about manifolds. :) – mimuller Jul 10 '21 at 17:28

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