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Mar 9, 2014 at 18:37 comment added Misha John: I see, this is the same as your argument. Incidentally, I was confusing a and the, not for the first or last time.
Mar 9, 2014 at 18:30 comment added Misha John: Then argue that Euclidean rays cannot diverge exponentially fast.
Mar 9, 2014 at 18:24 comment added John Pardon What if the foliating family of geodesics doesn't have any pair which share a point on the boundary?
Mar 9, 2014 at 18:23 comment added Misha Yes, this is impossible, since an isometric embedding preserves arclength of curves.
Mar 9, 2014 at 18:21 comment added Ali Taghavi Is not possible that the foliating geodesics would be mapped to a familly of half straight line approaching to the (deleted) origion?
Mar 9, 2014 at 17:46 history answered Misha CC BY-SA 3.0