Re: [math-fun] Relative convexity

Yes. For any smooth metric surface (or n-dimensional manifold) M, a subset X of M is "geodesically convex" if for any points p, q of X there is a unique shortest geodesic curve C in M connecting p and q, and C lies entirely in X. —Dan Jim Propp wrote: ----- Is there a notion of "relative convexity" that would make an ordinary torus consisting of points at small fixed distance from a large circle "convex relative to the circle"? Thinking about different sorts of polyhedral tori people have come up with, I realize that part of what I want esthetically is some kind of relative convexity, but I don't know what it should mean! -----