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Mar 6 at 15:58 comment added macbeth Thanks! I'll have to study this -- at first glance it's an explicit version for a different version of the Cheeger finiteness theorem than the one I asked about, but maybe there's a way of using it to answer my question.
Mar 6 at 14:26 comment added Julian Seipel In the paper of Stefan Peters there is an upper bound of $e^{e^{2n+8}}, $ but there is another assumption on the sectional curvature.
Feb 7 at 2:12 comment added macbeth By Brendle-Schoen, $\delta<\tfrac{1}{4}$ if it's not a sphere and not a symmetric space. So any of the other examples listed in section 2 of this survey of Ziller should have $\delta<\tfrac{1}{4}$. (And some of those are even-dimensional.)
Feb 7 at 0:38 comment added Deane Yang What are some examples when $\delta < \frac{1}{4}$?
Feb 6 at 21:01 history edited macbeth CC BY-SA 4.0
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Feb 6 at 2:12 history asked macbeth CC BY-SA 4.0