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Jul 3, 2017 at 10:53 vote accept Pete
Jul 3, 2017 at 10:53 comment added Pete @Mikhail: Thank you, of course! Wondering if it might hold true with more assumptions on $\mathcal{C}$. I'm interested in the case where $\mathcal{C}$ itself is the distance sphere of a point on the other hemisphere.
Jul 3, 2017 at 10:50 comment added Pete @Thomas: Only the surface was assumed to have nonnegative curvature.
Jul 3, 2017 at 8:51 comment added Thomas Richard Does it still have nonnegative curvature ?
Jul 3, 2017 at 8:37 history answered Mikhail Katz CC BY-SA 3.0