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Apr 30, 2014 at 15:05 history edited alvarezpaiva CC BY-SA 3.0
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Apr 30, 2014 at 15:04 comment added alvarezpaiva I thought about the metric midpoint (for the Hilbert metric) of the line segment. The distances to $a$ and $b$ are infinite.
Apr 30, 2014 at 14:22 comment added Suvrit I have a feeling that the answer is "yes", but I am not so well-versed in this area to qualify my answer. My hunch is, however, you might need to qualify the notion of "midpoint" (I'm presuming it is the argmin in terms of $d^2(x,a)+d^2(x,b)$)...
Apr 30, 2014 at 13:00 history edited alvarezpaiva CC BY-SA 3.0
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Apr 30, 2014 at 12:36 history edited alvarezpaiva CC BY-SA 3.0
deleted 2020 characters in body
Apr 30, 2014 at 11:34 history edited alvarezpaiva CC BY-SA 3.0
fixed spelling
Apr 30, 2014 at 11:29 history asked alvarezpaiva CC BY-SA 3.0