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Feb 1, 2019 at 22:50 comment added Andy Mack @DeaneYang: I don't quite see this (though I'm a newbie). Is it possible to do the calculation explicitly or something in this case?
Feb 1, 2019 at 20:42 comment added Deane Yang I think the exponential dependence might be realized for hyperbolic manifolds.
Feb 1, 2019 at 20:38 comment added Piotr Hajlasz @AndyMack I do not know examples showing sharpness of the inequality, but as far as I know this is the best inequality known. I would suggest to search who quoted the paper of Maheux and Saloff-Coste to see if there are better results.
Feb 1, 2019 at 20:34 comment added Andy Mack Is this known to be tight? In particular, is it know the dependence on $\kappa$ and $D$ needs to be exponential?
Feb 1, 2019 at 19:47 history answered Piotr Hajlasz CC BY-SA 4.0