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Feb 28, 2014 at 15:35 comment added user126154 now you may try to use the isoperimetric inequality for such periodic metrics.
Feb 28, 2014 at 12:16 comment added Bruno Martelli thanks! The adaptation of Alexander's proof does not seem totally obvious to me: you should use that R^3 has a metric which is periodic over a group acting co-complactly, otherwise the theorem is clearly false (since R^3 is not compact).
Feb 28, 2014 at 9:48 history edited Sam Nead CC BY-SA 3.0
Added further details, fixed statement of [MY]
Feb 27, 2014 at 21:54 history edited Sam Nead CC BY-SA 3.0
One step is vague - I pointed that out.
Feb 27, 2014 at 21:16 history edited Sam Nead CC BY-SA 3.0
notation improved, added transition.
Feb 27, 2014 at 21:01 history answered Sam Nead CC BY-SA 3.0